When you send a lot of ETH or USDT to a big exchange like Kraken, do they care if its come from a smaller non kyc exchange like Blofin? Do they care if it came from a bridge?
The exchanges system automatically credits your crypto deposit. But if your transaction is suspicious then the deposit is frozen. Be it small amount or big amount. I faced such a problem. I made a NEAR deposit from a wall on Binance but it was credited but my balance was frozen. Later I contacted the support and after giving them all the detailed proofs they unfroze my balance. When I asked them about this they said that my transaction was suspicious due to which my balance was frozen. So it can be said that any exchanger can freeze your balance if your transaction is suspicious
Your experience shows that exchanges do care about the sources of funds that is deposited with them, most of us wouldn't know this because we've not been victims of blocked accounts. Perhaps the exchanges ordinarily wouldn't care about the sources of funds but because of the mandate of regulations they wouldn't want to be in between suspicious transactions, that is my take on it. Some months back Binance had an issue with my government regarding suspicious transactions, it reached to a point where a Binance official was detained in a correctional facility for a long time before he was eventually released.