eventually there may be runs on various exchanges, and when people realise there is not as much BTC as they thought there was, this will cause a mad scramble to actually buy BTC.
What are you saying? I do not understand.
I mean that exchanger of BTC for $ do not have as much BTC as they may have received in. Eg they sold it or use it for other purposes, but are no longer in possession. So when you come looking for your BTC there wont be enough to go around. So while everyone account at an exchange may say they have say 10 BTC, if they were to all try get their BTC at one the exchange only has enough to give out 50% to everyone.
This would cause a run on exchanges(s) and probably push BTC way up.
Also Banks are regulated and they often go below the advertised 10%.