Welp, my few hundred bucks on bittrex have become 4-digit by now. I really need to get a hard wallet, thanks for the warning.
Back when I had to mail in my ID and stuff I had a similar frozen account problem, but this "we freeze until you do what we say" seems to be common practice. Skrill also froze 100€ of mine a few years back.
Yes, move everything to wallets where you control the key