I always had this question and now I want actually to know if it's possible to get the private keys of Coinbase accounts or Bit-x.com accounts and export them to import to another wallet .
Or simply the ability to sign messages using the adresses given on those accounts ?
Part of what keeps them so safe is not allowing you to get that private key. They then know no one got the private key from you even on accident.
Coinbase I believe even has some kinda insurance, which would be part of reason they don't release key.
I would actually believe the opposite of this. The fact that you do not have exclusive control over the private keys controlling your bitcoin means that you are less safe then you would be if you had generated and store your private keys yourself.
Both coinbase and bit-x are "web wallets" meaning that they do not keep your funds in a specific address, but rather will create an entry in their database when you send a transaction to them once it gets three confirmations, at which point they may use the outputs from your transaction as inputs to a transaction when another customer wishes to withdraw some of all of their bitcoin, or they may send your bitcoin to their cold storage.