What will happen is that the last standing non KYC exchanges will be shit exchanges such as Yobit.
Or decentralized exchanges like Bisq, which do not require KYC because they do not touch your coins at any time. Furthermore, because of their decentralized structure, it is near impossible for a government to shut them down - it would be akin to them trying to shutdown bitcoin itself. I admit they have a large problem right now with low liquidity and poor speed of trades, but hopefully as they become more popular in the future both of these things will improve.
There will always be a place for exchanges with full KYC procedures, because there will always be a demand from day traders for near instant trading with high liquidity.
As for Brave, I have used it for a while just for the sake of trying it out, but outside the earning feature it doesn't provide much utility over what some other browsers/extensions offer.
Agreed. I used it for some things, but Firefox with the right settings and extensions is superior in terms of speed, security, and privacy.
Brave is a trusted company with a good reputation
I'm by no means saying Brave is a scam, but giving someone access to your documents just because they are a "trusted company" is a pretty slippery slope. Quadriga was a "trusted company", until they exit scammed with millions. Many people considered Bitconnect a "trust company", until they did the same. Hell, Charles Ponzi was "trusted" by many individuals. Every scam that has successfully scammed people out of their money or information was initially "trusted" by someone.