The only problem I see, if you could even call it that, is that bitcoin "banks" (exchanges?) are restricted to being 100% warehousing operations since there is nobody to bail them out if (when?) they decide they can make more profit earning interest by loaning out the funds they are contractually obligated to hold.
If you want to avoid a run on your bitcoin exchange then simply don't engage in fractional reserve banking...or, I suppose, don't lose all your holdings to hackers.
Central banks have very little influence on the value of their currency once people lose faith in it, people will buy anything instead of holding on to their (usually rapidly devaluing) currency.
One thing every holder of bitcoin knows is it will never suffer through hyperinflation, ever.