I somehow agree that centralized exchange already became bitcoin bank, because most of the users are now using those centralized exchanges and have been upload their details in order to verificate their account, we can't avoid using echange without verifivation because they will limit some features such a minimum withdrawing or even do a trade.
Anyway. It depends on your crypto asset value. A lot of people use centralized exchange without verification. It is only when you have tons of btc that you begin to feel bothered about verification and besides why would someone keep a lot of BTC on exchange account. It is not save. I still prefer to use Centralized exchange because many of the decentralized ones are a piece of shit. From etherdelta to mercatox to forkdelta. From my experience, it is always rigorous to use and i dont like to upload or enter my private key on any exchange.
There is no issue in using centralized exchanges until they need us to verify our identity. Trading with smaller amounts onto those centralized exchanges would never cause any harm but if our daily trading volume exceeds above 2 BTC than the exchange might restrict you and make it mandatory to upload your KYC documents for verification which would never keep your anonymous anymore.
Decentralized exchanges would play a better role in such kind of situations as they would never ask for document verification but yet the benefits offered by such dex's are not that attractive to attract some traders onto the platform. Also there is minimum volume on such decentralized exchanges which would never make us find profits by trading with higher amounts because there would not be immense buy and sell orders to fulfill your orders.