I have thought of making a proof-of-concept "Casascius Bank" but where I accept no more than about 1000 BTC in total deposits.
The real goal, though, wouldn't be to become a bank. It would be to illustrate a proof-of-concept: provably secure depositing.
My "bank" would create cryptographic signatures on a daily basis proving in fact that I have every single bitcoin I say I have on deposit. Meanwhile, I would break down that 1000 BTC into "ranges" to assert that they are owned by specific depositors (but only in a manner where the depositors themselves can identify their own funds, not the public). For example, if I held 4 deposits for 4 people, and they were 100, 200, 300, and 400, then I would say that coins 1-100 belong to depositor 1, coins 201-400 belong to depositor 2, 401-600 and 601-1000 belong to depositors 3 and 4. I would sign and send messages to each depositor, which would allow them to reconcile, catch, and out me if (for example), I told two people they each own the same range of coins.
The real goal would be to help the public know they really can and should demand proof that their deposits are safe and sound and not fractionally pledged, the same way "provably fair gaming" is teaching us by example that we should demand, well, provably fair games.
In turn, this would cut down the number of "paper bitcoins" in existence (or rather, I should say, "bitcoin-denominated promises", because the "paper bitcoins" I have in mind - like bitaddress.org and bip38 - are actually close to the best kind of bitcoins you can have!)
Wow. That is an AMAZING idea. Given the thirst for bitcoin startups by VCs wanting to get in on the action, I think someone should really do this!!