But just like centralized exchanges NEED to implement KYC at some point (due to their government laws) or they will get shutdown, I think Brave actually needs to do that if they want to keep going with their idea of giving BAT tokens to publishers.
It's simply just a regulatory requirement for them to let some of their users accept and send BAT tokens in a legal matter.
Do we know why, though? There are hundreds of exchanges which trade crypto without involving fiat, which don't need KYC. There are crypto gambling sites which don't need KYC. Why is Brave, which also doesn't touch fiat, different?
There is noting free in this world. They let us to use their free product but we pay them without our data.
There are actually quite a lot of free services which will respect your privacy. Tails, Firefox, Tor, DDG. Have a look here for privacy respecting alternatives to most pieces of software:
https://prism-break.org/