Why not send BTC between web wallets? In this question, Is it possible to transfer BitCoins from BlockChain to CoinBase?, the answer implies that this is a bad idea.

But for me, this raises a question.

I like to Coinbase's tools for buying BTC straight through my bank account. But I like Blockchain's tools for backing up my wallet in standard encrypted format or cold storage. I would like to be able to exchange BTC on Coinbase, and then migrate those to my wallet on Blockchain.

It seems to me that whether I happen to own both accounts is irrelevant. It seems exactly the same as any other BTC transaction. Is there actually a reason against this?

Is it possible to transfer BitCoins from BlockChain to CoinBase?
Actually, the answer on the linked question states that it is possible, but that one should be careful not to return money back to the sending address, because said sending address might not be associated with the personal wallet, but rather owned by the service itself.