Bitcoin is has a supply limit, so that taken together with it's technical features such as a proof of transaction and digital-ness makes it highly valuable in an economy where more and more transactions take place in the digital rather than the physical space.

I'm sure there's a better answer, but that's the best I can muster with my current knowledge on the matter.

I think a better question is "given the rarity of bitcoin, why wouldn't people value it?"

Also, as for the confidence thing, bitcoin is no different than anything else in our economy. Our economy is built on confidence.

Yes, that could happen.

By 'regression to the mean', I just meant that Bitcoin prices come to reflect average desirability. So even huge events like the pump/dump bubble that Mt Gox (or its infiltrator) created eventually damp out.

Right now, I gather that it's largely Chinese investors who are pushing Bitcoin prices up.