I am posting it now because only recently, after AMD released legacy Catalyst 13.1, I could play TF 2.
I have noticed the loading take too long, not only to the main menu but also to start every match. I remember when I was playing it on Windows, the loadings were not fast, but on Linux it is taking more time.
I saw it happens with other people like you can see on this thread:
Here are my specs: