Coinbase is a centralized exchange and a custodial wallet. Therefore, they have to regulate transactions and they have the right to suspend/terminate/block an account.
And it's because they're so regulated by the US government that they are actually "safe". Ever since I've been a member of this forum, I've seen tons of scams perpetrated by exchanges that weren't regulated, and with basically no oversight they were free to steal their customers' funds with impunity.
And yes, Coinbase can terminate anybody's account, and they don't have to give you a reason--but I don't think I've ever read about cases where closed accounts resulted in lost funds on Coinbase. That's not something a highly-regulated exchange could get away with. Compare that to an exchange like Yobit. It's remarkable that they haven't pulled an exit scam yet.
I wouldn't be surprised to see coinbase blocking an account, however, when they block account, they give back the fund.
Yes, I had that happen to me with Coinbase and I didn't lose my bitcoin.
OP, I understand the concerns you have, which basically amount to privacy issues. Even if I could reinstate my Coinbase account, I wouldn't--and for the reasons you pointed out. I don't like banks or anyone else watching what I'm doing with my money.