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?
They 100% care, without a doubt. I remember few of my friends got a message from binance asking them to explain why and how they are regularly receiving money from some places. They had to explain that it was because of the a campaign, and they let me be, but if they didn't have proof, then binance would have blocked their account.
While you may not get caught every time, that doesn't mean that you are doing something they allow, you are just doing something against their rules and not caught yet, that's it. So, they do care where the money comes from, depends on where it comes from though, if it's something illegal then they care, if it is not illegal then they do not care, that's the most important part of it, and I believe that matters a lot.