Can a bitcoin bank solve the problem of intensive value fluctuation caused by hoarding?
Saying people are hoarding bitcoins is out of focus: they are simply "not spending them" because there aren't enough ways to spend them.

Allowing loans wouldn't improve the situation, since there still wouldn't be many ways to spend those loaned bitcoins.

Finally, bitcoins already are a currency subject to deflation, and they are also (more or less) constantly gaining value against traditional currencies, so just holding them increases their value.

To sum it up, not a terribly good idea, and definitely not ground-breaking.