One of the recent past threads on clothing gripes and poor quality did suggest there has been a cotton shortage in recent years, but as you say, it's clearly not the actual reason for why so much clothing intended for women has switched to synthetic fibres.
I'm willing to both believe and accept that viscose is a much better fabric than polyester - but it still doesn't make me willing to buy viscose, generally speaking. I don't mind those Heattech long-sleeve things from Uniqlo, which are synthetic, but I'm only ever wearing them as a layer over a short-sleeve top, not directly on the body. When I've tried on viscose tops in store, they weren't for me. I can't wear most polyester tops, I really hate the feeling of it on the skin after a short time. Definitely agree about the 'recycled polyester'. It's not a selling point that it's not cotton! It's a bad thing!
Cap sleeves and too short tops. I find that even a lot of tops that aren't specifically cropped are too short on me (as in, seem fine if standing straight but you want to allow for movement and it riding up), but the cropped style I actively think is stupid. Too many tops are too narrow on the shoulders and across the back for me too, but that's not a style.
Weird cut-away holes. The apparent inability to grasp that not everyone wants to show off skin. For summer, I find that most sleeveless tops that have a higher neckline (I don't mean turtleneck, just up around the collarbones) compensate for having to use a little more fabric there by cutting away the fabric in the back.
Polo pique fabric. I do like some polo tops, but only jersey polos. Often if you're looking online, it's not clear which it is.