Interested to see where this all goes. About me: I'm a student. I lift twice a week, indoor climb once a week, gymnastics gym once a week, and run once or twice a week. I also bike to and from work every day, and skate around my campus.
I feel like I may be in abnormal in not caring too much about performance fabric for workout purposes. My shitty old college shirts work just fine for a lifting session or a run. Maybe if I were lifting for much longer than an hour or running much farther than 3-5 miles I'd want serious performance, but gym clothes are just gym clothes for me. I've been wearing the same pair of champion basketball shorts to the gym since 2011 and they look like I could've bought them yesterday. For running, I have a pair of nike (I think?) running shorts that do the job, and a handful of synthetic shirts from the odd 10k that are a little better than the cotton ones.
My first thought when you bring up performance fabric t-shirts is heat.
I am terrible at hot weather. I'm not a big shorts guy so I'm usually wearing light jeans and a t-shirt. If I so much as walk quickly my cotton t's - pistol lake t's included - are soaked through almost instantaneously. I remember having to run to a class to give a presentation last year and knowing this was the end. I had to give the presentation with my shirt literally dripping sweat as if I'd finished a race.
So it's less the gymwear and the "versatile" part that gets me. I'd love lightweight, synthetic t shirts that look good over jeans (or shorts, if I give in) and are good for hot weather or a hike. Adventurewear that I could wear off the hike to a bar too. I tried uniqlo airism, but the fit was odd, the material was shiny, and it just didn't work for me. For the shirts, I'm not a huge fan of the raglan sleeve look (wait, are the henleys raglan sleeve? maybe it does look alright). As for the shorts, I'll wait and see..maybe you'll make a pair of shorts I actually like wearing.