Ah, the lost art of typography!
Most of the changes you mention can be done in AE and should be done by any discerning typehead. Really, only "perfect pixel alignment" for web fonts will be the only things you can't do in AE (or in illustrator and then bring into AE). Once the creators start messing with counter heights and x height differences, I'm sorry, it's just not the same font anymore- same family maybe but not the same font. We work with a lot of fonts that have been slightly warped for a corporation but based on a classic. Its shocking how little differences can make a huge impact on how the type looks in a block. While some fonts have been designed for the web, there are a few hundred years of refining that have gone into some classics that (when set right ) should not be ignored.
But all that aside, I think it mattered more when a high rez screen was 1280pix or less, Now with HD and 4K there are so many pixels per sq inch, IMHO, you should apply the rules you would apply if you were making a print piece that was 24" diagonal (or whatever your viewing size will be) - the human eye hasn't changes that much since Gutenberg.
One of my guys says "ya but there are so many screen sizes that people might be looking at this on". True, but how many design houses will adjust the letter spacing for the postcard they just made out of the poster you just carefully typeset. The browser should be handling the corrections needed for ultra small screens vs larger ones and if that is built into the font, great, but with the need to make a splash and be different, I doubt many "different" fonts have that feature.
I think people have forgotten they still need to set type, or probably more accurately, were never taught that things like letter spacing and x heights and kerning or ligatures even matter. And with no one wanting to pay for fonts these days I think it's a losing battle to expect electronic display versions from a virus-laden freebee.