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?