Did I shoot myself in the foot by purchasing through KYC exchanges?
I am assuming you bought Bitcoin as a long-term investment, so the answer is
no. In any case, if you have followed the "Know-Your-Customer" procedure and purchased BTC on a legitimate exchange, you can withdraw your coins to a cold wallet to avoid the risk of losing funds due to a possible hacked trading platform.
Is there a way to reverse the damage? Perhaps through things like mixers etc? What are your thoughts on those?
Keep in mind that the cryptocurrency exchange can
monitor the public Bitcoin blockchain and
track all transactions associated with the BTC address you provided. I've heard that some exchanges blocked their customers' accounts when they sent withdrawn coins to the mixers, so beware of such activity.