You can still transact with Bitcoin using your own wallets against other exchanges/vaults. That's the entire point, Coinbase, like a (lower case "b") doesn't control the supply of Bitcoin, any more than precious metals bullions control the supply of gold despite their issuance of "gold certificates". Like any (lower case "b") bank, Coinbase can engage in bad behavior, and users are placing their trust in Coinbase to not do that. But those users aren't placing their trust in Coinbase to drive the monetary policy of Bitcoin, in the same way that the gold hoarder placing their gold bars in a Swiss vault doesn't really have to worry about the operator of the vault creating gold out of thin air. That fundamental fact drives the collective belief in the value of gold; as well as Bitcoin.
> * the new owners of those 100 bitcoins can roll down to exchange X and deposit them and accept 100 claims against exchange X in return
You can't deposit that purchased BTC at another exchange unless you cash out of Coinbase, because you don't have access to the private key, Coinbase does.