Cotton has its place in desert hiking–get that T shirt wet and you have your own personal swamp cooler for 20 minutes or so. In fact, it will dry too soon in that high heat-low humidity environment!
On the other hand, I am not a fan of cotton in the mountains and foothills where I hike (Pacific NW). A hot sunny day can turn foggy and cold in less than an hour. Should that same T shirt get wet, it will never get dry. In the meantime, it has absorbed its weight in water, which you'll have to carry. Personally, I'd rather carry my water in a bottle than in a soggy T-shirt!
One compromise is a woven fabric (not knit) shirt of cotton-polyester blend, which I used to wear for hiking, in hot weather. Unless it's really heavy fabric, it dries faster yet definitely is more breathable than all-cotton. I like a nice loose, floppy fit for more ventilation.
I would still wear a cotton-polyester blend floppy shirt in hot weather except that I now own a heat-stroke prone dog (mostly Lab). I therefore no longer hike when the temp gets above 85* F (29 C). Instead, I start at the crack of dawn and plan to seek deep shade and water for a nice long siesta by 11 am.