For sports shirts the advertising is literally part of the shirt design, if you remove all adverts with a razorblade now you'd wasted a lot of money on a shirt with huge holes in it.
A friend of mine used to do this with products that self-advertise when he was younger (I notice his Tilley hat is unmolested, presumably he had now stopped), but it doesn't really make sense on say a reproduction football kit.
I reached a certain point and decided that a plain single color or striped cotton tshirt from kohls looks and feels as good as any plain single color cotton shirt that might have a swoosh on it. Bonus the no logo version is usually cheaper as well.