Good idea. There are some minor issues with it, but I don't think it's possible to easily fix them.
There are also some minor dangers for the currency as it could collapse if one of the early miners sold most of their fortune on public exchanges, but last time it collapsed, it grew back up and stablizied as the concept is good and thus people can put their trust in it.
>>2
There's no difference there compared to regular fiat currencies: you choose to trust that you'll be able to exchange them, and people choose to exchange other things they find of value (gold, work, services and so on) for something which has no intrinsic value, but once everyone thinks something has value, it has value by shared consensus and thus it can be used as a means of exchange. Bitcoin is no different.