This would also not work (assuming other people still leave their money at exchanges), this because fractional reserve bank sort of create new money of thin air, inflating the currency, and so mess with even those without money at banks or exchanges.
Which brings us back full circle to the point I made in my first reply in this thread here:
The only way to avoid being subjected to fractional reserve is to hold your own coins. The only way to completely stop fractional reserve systems altogether is if everybody held their own coins.
As long as a significant proportion of users are happy to let third parties store their private keys and therefore have complete control over their coins, then there will always be the possibility that the third party is practicing fractional reserve banking, regardless of whatever kinds of checks of balances you put in place. The only way to prevent is for everyone to hold their own keys and their own coins.