Mixing all of the 'coins' for all of the accounts together is, I think, an overall plus for privacy. True, you might receive coins from somebody and be able to figure out "Hey, they sent me some of exactly the same coins I deposited in my BigBitBank account yesterday! They must have an account at BigBitBank, too!"
But mixing all the accounts' coins together makes it much more difficult to figure out where any user's coins came from, or, if you know where they came from, where the user is spending their bitcoins. Unless you can subpeona BigBitBank's records, of course...
Yea that makes sense, so if I sum it up, with accounts :
- (-) I can pretty accurately tell if some other address belongs to the bank pool (even if I'm not able to check an arbitrary address)
- (+) I can send coins from addresses that didn't originally receive the coins, making them very hard to track through BBE
Sounds fair!