Here's what I've never seen: Serious extrapolation of the cultural/social side effects of having universal healthcare in the US. Odd, since it comes up as a side effect/butterfly in people's timelines alot.
Specifically, I'm thinking the effects of reducing both the BOOTSTRAPS/mah personal responsibility culture, plus severely weakening one of the 'sticks' to use the old carrot and stick analogy used for enforcing 'middle class' conformism regardless of decade*. The conclusion is obvious: you get a country that'd be significantly more socially liberal than OTL, but not in an OTL sense -- think a combination what we see from OTL western countries that weren't saddled with puritan settlers with Japan's willingness to allow quite alot of stuff that well 4chan posters would approve of but would likely get called 'problematic' if you're respectable enough to have a blue check of verification. The social liberalism of apathy/being ah latitudarian re: people's hedonism rather than the dominant Obama/#MeToo/Silicon valley strain of liberalism. The reduced inequality, if still higher than developed nation levels would have bigtime cultural effects. The reasoning is simple: There'd be more "poor but not quite struggling", solid working class andyes even middle class people and fewer outright poor people than OTL. It'd mean more sensationalist media and less intellectual/faux-intellectual stuff. TV or media in the 2010s OTL is largely aimed towards the upper-middle classes, in TTL this wouldn't apply anywhere near as much due to the differences in consumer base. For a small example of what a more prole/working class-aimed media would look lilke, think of the stuff we saw in the less unequal 80s or 90s vs now. Yeah, more 'edgy' media, more random/pointless sexuality, more gore, more anime and much less self-referential/postmodernism/"relevant" political commentary. That's just the cartoons for kids/teenagers. This would of course apply to other countries too, even ones already having UHC by whenever the US gets it due to sheer influence of Hollywood.
We've seen economic side effect discussion sure, including analogies for other countries with it but not gone deeply enough -- with the choice of keeping the budget deficits well (pre-reagan) normal and medicare* running smoothly or adding to deficits with rent-seeking laws*, it's obviously going to be the popular program kept. Another factor that'd reduce rent-seeking or monopolies would be the fact that business would no longer have to pay twice for health benefits -- buying group plans *plus* being taxed for medicare/medicaid. Going by the the increasing desperation on the part of business to find new revenue streams OTL*, this would mean a visibly different experience for US consumers. There's no shortage of articles out there about how countries with UHC are often more entrepreneurial than the US in some ways, so that'd apply. Actually, it'd be amplified given there being less pressure for 'stable' markets* and government encouragement of oligopolies/monopolies meaning more competition in place.
Lastly, Going by the most likely timeframes during the cold war, the idea that some truly large* expansion of the welfare state wasn't a one-way trip to FULL COMMUNISM and the gulags would do "funny" things to the conservative coalition. It took the Baby Boomers OTL aging to the "Get off your lawn" age and generations X/Y experiencing the side effects of reaganite economics to produce an attempt at a troll candidate with Ron Paul in 2008, to electing Donald John Trump in 2016. Somehow, going by the likely effects on the fusionist coalition it lasting 24+ years after the end of the cold war, and close to 40 after Reagan's election in this TL isn't happening. The possibilities are well.. I could be openly trollish and say "Trump, Earlier but with more support and someone more tactful to implement his ideas" but there's more than that -- Eisenhower-nixonism forever? Nixon's "New Majority", The Pre-reagan GOP aged into place? Up to whoever does this
* From grey flannel suits to plaid shirts and duck dynasty beards, the look changes but the middle class puritanism doesn't.
* Well, why not? NHS wouldn't fit the US, too ah clinical.
* Airline fees, paid online for videogame consoles(Microsoft started it, the others followed), putting energy into finance, being extremely cautious re: bad PR
* Read: no competition, or if competition is allowed it's on gentlemanly terms. Think ISP monopolies as exhibit A of course.
* Medicare/medicaid were smaller than a full-sized UHC program would be
* insert list of quite a few of regulations. I'd expect there to be alot weaker state licensing boards/insurance commissions and copyright law in TTL. Not so much decline but much slower expansions post-adoption of UHC.