Bittrex BTC Withdraw

Hey all got a question. I read that people say you should never withdraw btc from a gambling site directly into coinbase. Such as if you have btc in coinbase and want to deposit it into a gambling sites, always use a bitcoin wallet or blockchain right?

Also the opposite holds true such as if you withdraw btc from a gambling site, always, give them your bitcoin wallet address... then you send the btc to coinbase. First off, that is still true right? And when people talk about coinbase banning their accounts, which way is it usually because of? Going from coinbase to gambling site or gambling site to coinbase?

Now i just thought about something else. When i withdraw btc from gambling sites, i would have them send it to my bitcoin wallet etc. Then if i want to send the btc to say an exchange like bittrex, i would then send the btc from my bitcoin wallet to bittrex. Does anyone know if there are any issues if you withdraw btc from a gambling website and the btc address you give them is bittrex or say binance? Or the other way around such as i have btc in bittrex or say binance... i send it directly to a gambling site without using my bitcoin wallet as an intermediary? I ask this because if i could do it that way, well i dont have to wait for the btc to be received on my bitcoin wallet... then it takes a while to send the btc to bittrex or say binance. Thus not only do i save fees, well i don't have to go from gambling site to my btc wallet and then to bittrex/binance.