They can do that but then nobody will be able to trade on the exchanges.
Exchanges just have 1 Steem Account, just like yours or mine.
When you sent Steem to an exchange it's held in this 1 account, only the memo you send with it identifies it as yours as an IOU on the exchange.
When Steemit inc. sends money to Bittrex they can use it as a tumbler. When it comes out and is send to another Steem account nobody knows who owns it.