This is a pretty shallow suggestion, and in all honesty, we are our own banks.

What you suggest is rather... Well, not a good idea. Debit cards are much better than credit, but we don't need them when we can just have all our crowns in our inventory. The bank being across players is not a great idea, especially since you could just transfer all your money from one character to another at will (which you can do anyways if you mail yourself all your crowns). Energy is already shared across the entire account, so that doesn't matter.

HOWEVER... It would be really nice to have a bank of sorts that would be accessible to single players. This item could be added to town square or the Bazaar, and have a new NPC knight/monster be in charge. This bank would let you deposit crowns, energy, materials, and other unbound items. For a fee, you could store bound items, but it will cost X energy every time you deposit/withdraw it. There would be no interest gained, and no loans given out. It is essentially a "guild storage" for individual players.
This system could also do a few cool things for you, such as: Donate X amounts of crowns every week on Y day(s) to guild upkeep, send mail massively to other players (double as a post office, anyone?) with 10 crowns per player added (first person would be 25 crowns. For each attachment in each mail add another 85 crowns per person. This makes mass mail sending cheaper through this method, but also cheaper without the post office/bank for single letters), and maybe hold give-aways or special missions when players accumulate X amount of crowns in the bank. When using the auction house, you could also view how many crowns you have in the bank, and for an additional 25 crowns you could bid money from your bank.