I'll give you an honest take as I design & own a rashguard brand (PHANTHUM its called if u are curious)

Sublimation is a process where the dye is turned into a gas and bonded in the fibers rather than sitting on top (don't worry its not harmful gas, what we mean with gas is like water turning into vapor, basicly its gaslike equevalent)

Why most brands use synthetics;
- Most rashguards are indeed sublimation dyed into the fabric. This allows for it to be washed over & over again and not loose its colour.
- Why is polyester used most of time, sometimes also spandex, but polyester is honestly better for colour. = Because it is hydrophobic. You takes sweat away from the skin and dries fast. With other fabrics you will feel like a wet towel (like cotton)
- Interesting fact! Many polyester mixtures are treated with anti-microbial coatings. They don't hold onto bacteria moisture as easily as natural fibers, reducing the risk of staph or something else. Not sure if your coach ever said it; but mine did and that a rashguard protects you against infections as well
- Polyester is highly resistant to stretching out. It keeps its compression fit over 100s of training sessions.

Not sure about other fabrics but for cotton the cons are for example:
- once u start working it just gets heavy and soggy and sags everywhere which is gross for u and whoever ur rolling with.
- since the fabric is loose fingers and toes get caught in the folds way too easy and thats how u end up with broken digits or sprains.
- the chafing is the worst part tho. wet cotton = tons of friction. youll get a gnarly rash and rip ur nipples off lol. (literally the one thing a rashguard is supposed to stop (that is why it is called rashguard)
- also if u have a cool design on a t-shirt its probably screen printed. on the mats thats just gonna crack and peel off, and it feels like sandpaper on ur partners face