FUTL is essentially a polemic disguised as a science fiction story. FUTL ended up being the basic blueprint for Heinlein's "Future History" series of novels, the one which formed the basis of his "primary" SF universe--the one with Lazarus Long and the Howard Families.
In his youth, Heinlein was a liberal Democrat. This was at a time when Socialism was the new trend for goverments worldwide; after World War I, particularly, Socialism took off in Europe, and many on the left side of the aisle in the US wanted the US to follow Europe's lead and also become socialist.
The root governmental principle of Nazism, besides Fascism, is Socialism; it's even in the title: "National Socialist Party", goes the translation. Lenin and Stalin cloaked Communism in the mantle of Socialism. Everyone wanted it because all the politicians told them that it would be better than lassez-faire capitalism!
The Democrats have been pro-Socialism since at least the early 1900s, possibly a bit earlier. Their desire to build a "worker's paradise" was oddly coupled with "Jim Crow" legislation and racism that had been deeply entrenched since before the Civil War. A lot of Democrats came from the Deep South, both before and after the Civil War. Their party was the party of government regulation, taxation, and Socialism...but only for white people.
This is the dirty little secret of the Democrat Party, which no one ever talks about. The Civil Rights Act of 1964 was passed by a largely Republican Congress; many Democrats voted against it (including Al Gore Sr, VP Al Gore's father). Lincoln had to free the slaves by executive order.
Heinlein himself had been born and raised Democrat; and when he got out of the Midwest and went to Annapolis to learn to be a Naval officer, he learned much about history, language, mathematics, and culture. He trained as an engineer and graduated from the Naval Academy a brand-new 2nd Lieutenant in the US Navy.
Then he got tuberculosis.
Discharged due to his medical condition--this was years before antibiotics or even sulfa--he turned to other things. He was a politician for a while; but he also had the desire to write. And history was made when he submitted his first-published short story, Life Line, for publication.
Years after his death in 1988, and after the death of his wife Virginia, the manuscript for FUTL was found, cleaned up, and published.
FUTL described a paradise on Earth, where Americans were rich and happy and well-adjusted, and not plagued with a high crime rate, inflation, or poverty. People were automatically guaranteed an income, and if they chose to work, they could easily be very rich. Everyone was polite to everyone else.
The story was a typical "fish out of water" story; Heinlein borrowed heavily from H.G. Wells' When the Sleeper Wakes, although the main character was in a fatal car wreck, which catapulted him into the future; he found himself in the body of a distant descendant and proceeded to explore the world he'd found himself in, guided by the attractive female lead--who was the basic model prototype for just about every female protagonist Heinlein had ever used.
Money was no longer controlled by banks. (Here we see the "anti-capital" element of Socialism in play.) The economy was regulated by the goverment; every citizen of the US was given an allowance, a "dividend" which was determined annually by the government. In essence it was a monthly stipend that every citizen of the US, rich or poor, received. It was always guaranteed to be enough to subsist on; you might not live well but you would not starve and you'd have a place to live.
Anyone could be in business to sell whatever products they wished, at whatever prices they wished to charge. However, there was an advantage to following goverment guidelines and selling products at 10% under retail price: the government would pay them the difference after the sales receipts were tallied.
Inflation was carefully controlled by this system--called Social Credit Theory by its creator, C.H. Douglas.
All of that sounds very good; but it wouldn't work.
The system assumes that all people are responsible adults who won't spend their dividend foolishly unless they have other income. It also assumes that people won't be criminals.
Heinlein's utopia deals with crime by treating it as mental illness. In the story, the main character sees his new girlfriend with another man and--as any man from his era would do--punches him in the snoot. The other man calls the police, our hero is arrested, and taken to a hospital. He hasn't committed a crime; he has had an "atavism" and requires medical care.
I should mention that medicine was 100% socialized in Heinlein's world. I do not recall how Heinlein's utopia paid for all this, by the way.
There is an alternative to medical care: he could choose Coventry. Choosing Coventry lets him retain his personality as it is, but US society will withdraw itself from him. Coventry is a largish area somewhere in the US which exists in a state of anarchy, more or less; there is a society in it which we see in a short story Heinlein wrote years later.
As for FUTL, our hero mistakenly thinks he is confined to the grounds of the "clinic", but he is not; later he learns that his doctors allowed him to think so but would have told him the truth had he asked. He is "cured" when he goes to visit his girlfriend, sees her rutting with the other man, and tiptoes out rather than making a scene.
What all this amounts to is, in effect, a kind of soft-pedaled re-education camp. Everyone must be nice to everyone else; otherwise the government doctors will "help you get better". You are not required to stay in the camp, but if you fail to show up for your therapy you will eventually be found and sent to Coventry. (Since you cannot earn or spend money in that world without leaving a record of it, you're relatively easy to track, I might add.)
Marriage is effectively nonexistent. "Free love" is the order of the day and there are no rules limiting sexual behavior. In many ways, it is the Libertarian ideal in that respect, and the only reason our hero has his "atavism" is because of his old-fashioned ideas and attitudes.
The problem with stories like this is that they assume that everyone will place nice. Heinlein argued, in later stories, that "Man cannot be tamed", yet in FUTL he seems to be saying the opposite. There is little crime, little poverty, little suffering; elsewhere in the world is utter disaster and misery but not in the USA.
The story ignores the basic fact that some people are stupid and incompetent. It's a fact of life; for every genius there is at least one utter bonehead (probably two or sixty). While many people can evaluate their own symptoms and think, "I have a cold; I'll just take aspirin and take a day off from work," too many will say, "OMG I'M DYING I NEED TO GO TO THE HOSPITAL!" ...when they have a simple cold and need only fluids and bed rest.
The medical system in the story would be overwhelmed by people who thought they needed urgent medical care for minor problems. And forget the mental health industry; it would be choked with stupid people who wanted their hands held by therapists after their parakeets died.
To say nothing of the fact that there would be people who spent their "dividend" checks on booze and drugs, and who would then have nothing left to pay the rent. These people would be an even bigger drain on the medical system. They would binge for however long it took them to spend their dividend; then they'd check into the hospital, "sick" (ie hung over!) until the next check came. A lot of them would die, though, sooner or later; the system in FUTL made no attempt to prevent natural selection. People who used illegal substances would end up either either in Rehab or Coventry, too, of course.
There seemed to be no mechanism to prevent recidivism. It seemed that one could commit exactly the same crime, over and over again, and just have to go to therapy. Would anyone actually change his behavior? Or would people learn how to fool the therapists into letting them back into the "real world"? Why change for real when all you have to do is act the right way long enough to get your release papers signed? The "Bingers" from the previous paragraph could commit an atavism to get sent to the hospital, in fact:
"Hey dude, I don't have any money left. I'm gonna slug you, okay?"
"Okay, but next month, you gotta buy me a bottle, okay?"
Combine "free money" with "free health care" and "free love", and assign no actual consequences for bad behavior--the population would explode and "utopia" would turn into a pile of shit...assuming that it ever managed to "rise above its capitalist beginnings" in the first place. Crime would be rampant and uncontrollable, and the "right-thinking" elite would end up having to utterly insulate themselves from it.
You would not get the orderly society that Heinlein describes in FUTL, not without some extra-heavy Stormtrooper action. It would be a police state; it would be a police state with flowers and happy faces, but it would still be a police state. Binging would be illegal and get you sent to Coventry. Having too many children (ie failing to take your birth control) would get you sent to re-education camp, or Coventry if that didn't work. Every citizen receiving a dividend check would be required to buy a certain amount of food and shelter with that dividend. Children would have to go to government schools--no exceptions!--in order to learn how to function in "modern society", and they would have to prove they could handle the responsibility of a dividend check before they were allowed out of the schools.
Contrast the FUTL world, then, with the world of Starship Troopers (ST). In ST, we see a completely different type of society.
In ST, driving drunk is not an "atavism" or "antisocial behavior"; it's a crime which is punished by five lashes from a whip and public exposure in stocks. Antisocial behavior is not "treated" but punished. The story is most eloquent on the advantages of corporal--and capital--punishment; and ST was as much of a polemic as FUTL was: by Heinlein's own admission, ST was written after Eisenhower signed the Nuclear Test Ban Treaty.
In his later years, Heinlein left the Democrat Party and became a Libertarian, in all but name. (See my prior entry, I Like Cheese for a discussion of this phenomenon.)
Churchill said, "If you are twenty and not a liberal, you have no heart. If you are forty and not a conservative, you have no head." Heinlein simply had both.