sure but these "off chain" transactions are not really Bitcoin, but the exchange's promises of Bitcoin (or whatever cryptocurrency under discussion). As long as

sure but these "off chain" transactions are not really Bitcoin, but the exchange's promises of Bitcoin (or whatever cryptocurrency under discussion). As long as custommers succeed in end-to-end conversion the distinction is moot, until they fail to succeed in this end-to-end conversion. So still a commercial bank can not fractional reserve bank BTC, only fractional reserve bank promises for BTC. For a while people may fall for such a scheme but players learn...