I'd ask why couldn't use fractional reserves (ie: loaning out bitcoins) and make a profit that way (if, as earlier mentioned, one could figure out a way to ensure that people would pay back their loans)?
Because the currency is too unstable. There's always a risk the currency could jump up a large amount in a day, thus causing a significant fraction of your loans not to be paid back. This would mean your 'guarantee' wouldn't be worth the paper it was printed on.
The only way, for now, to do a fractional reserve with bitcoins is with offseting shorts. You can't do it by loaning the coins out. (And you would have to put interest clamps on. For example, if you deposit BTC worth $100 USD, and BTC doubles in a week, you can't get $200 USD worth of BTC. They may not even be available at any price.)
And even if you didn't do that, I'd argue that there is an inherent value in having access to a large quantity of bitcoins that could lead to monetization opportunities. Hell, if enough people use the bank, one could even make a decent amount of money of advertising alone. Also, something like this would be worthwhile in my opinion, having a bank is also worthwhile just as a way to add legitimacy and stability to bitcoins that could pave the way to larger-scale adoption by the general public.
There's no advertising revenue in the world that will keep you solvent if bitcoins shoot up 35% before you can buy enough of them. (Even if you react instantly, there's no guarantee you'll be able to buy enough.)
That idea is a non-starter for now. Again, unless you're willing to accept interest clamps (may have to pay you back in USD, may not be able to give you 100% of the increase in BTC value) and if you can find enough people willing to sell BTC short.