KYC exchanges are exchanges that guarantee the safety of their users, there may be some exchanges that do not use KYC, but as such these exchanges are less secure, and look un professional, I really like KYC exchanges because they are of good quality and professional.
Binance won't force you to do KYC but you're limited with how much you can withdraw. Despite that, they're still a good exchange and also considered as one of the best exchanges although if you want to increase and upgrade your account, you really have to do KYC.
Is there a way to reverse the damage? Perhaps through things like mixers etc? What are your thoughts on those?
If you're not confident with your privacy and you think that there's a need to let through a mixer then just do it. Because if you won't do it, you'll keep worrying with that matter. So just do it and have a peace of mind.