As for hospitals, it's simple. If you don't purposely slow your growth you will almost always be happiness capped at the Industrial era. What use is excess food when it gets sucked up so quickly? There's always a better building.
As others have mentioned, that is true only if you have a lot of cities (and no happiness...which the overhead of per-city unhappiness makes even worse).
Based on your posts including the "ignore happiness" thread, your playstyle is to own every hex on the map. The problem is not just that not all hexes are created equal, but that older and more infrastructurified cities multiply those hexes.
Perhaps not all maps allow for sufficient super-city-sites for a fewer city strategy to be stronger, but nevertheless, 1 pop is much better in a good city than a bad city! A bad/new city 1 pop gets you say 2 hammers, in a production city it gets you say factory + railroad + windmill + hydro + forge + ... = ~5 trillion hammers. In addition the production city already has the rax-type buildings so each multiplied hammer is also effectively multiplied.
That leads into the second problem with a new city, that inferior count of 2 hammers has to waste time doing things other than building super units: building the monument/temple/library/granary/forge/stables/barracks/armory/... that your good production city would already have..just to one day be a production city! It will forever play catch-up (you will have researched a new building by then, which the production city will build in 0.3 turns or so).
The only thing I can think that the junk city accomplishes is with the faster initial growth, you would perhaps gain a 3 beaker advantage (lol), that is until the production city grows 1 pop and gains all the science multipliers it built while it was bored from having too many hammers.
I believe you have a sort of self-fulfilling prophecy in your games..always maximizing cap and military, so what need is there to make an especially good city? Just take more, thereby increasing the maritime bonus and keeping you at the cap (or well past it..)! So long as your gold income is enough to cover upgrades, you are set for the rest of the game. That doesn't prove it's the best strategy though, only that the happiness penalties are weak.
Perhaps if instead of puppeting every last piece of junk, raze them and use the cap to add a pop to your 250% science city or your 83% gold city or whatever. I would only keep a puppet as a FOB (forward operating base) overseas, healing, razing, and repeating as more land is conquered, or if there are sufficient turns left and the city site is THAT good.
It's possible you in fact have the best strategy (especially for maps lacking good city sites), but you may not. One can maybe/probably/hopefully??! assume the following: a future patch will weaken maritimes and strengthen happiness penalties. If so, the high quality city strategy will HAVE to be better, so given that, one should grow a good city as opposed to capturing a loser city from Arabia just so that 70 turns later it might build a monument. Given THAT, you would want a hospital.
Lastly, it's even possible that later on in the game, as your puppets have become more advanced, they are still much worse than your very best city, such that it could even be worth razing a semi-big city to allow a VERY good city to grow. Granted this is somewhat extreme, but it's not at all obvious that hospitals are worthless.
EDIT:
In response to what you just said, that's because maritimes are too good. Even if it could eventually be shown that my argument is flawed and that hospitals aren't worth it, it would be because as you said, maritimes give huge amounts of food, not because the hospital itself is in anyway not amazing. (A similar argument applies to the granary).
For me, good sarcasm contains both truth and good humour. But one has to be careful on these forums because in here people are smart.
