I'm probably about to spout shit but if anyone can correct me if I'm wrong this would be appreciated!

So bitcoin isn't 'anonymous' in a sense. You can see where bitcoin moves between wallets etc. It's a case of who owns the wallet can be kinda anonymous. As for coinbase, it's not really a wallet it's kinda like a large pool of bitcoin and they say you have x amount of it. Similar to Paypal, you don't actually have the money they display it's in one of their main accounts. As for your personal information and IP, all that kinda stuff is protected by some form of the Data Protection act (for the UK, some equivalent for their country etc). So they are inclined to keep that data private and secure.