If a Linux desktop distribution was ever commercially successful in a meaningful way, the first thing that would happen is black hats would create fake copies of the distribution with spyware and adware installed, or worse. We've seen this time and time again.
If you don't have a trademark, then you can't do anything about it. This is also the reason why Linus Torvalds has a trademark on "Linux."
It's all very well and good to say "well, those people are stupid. They should have gone to the REAL fedoraproject.org." But if you don't have a trademark, there's nothing stopping the black hats from registering therealfedoraproject.org and putting the badware there.
tl;dr Trademark law exists for a reason and it's not evil.