I have seen and experienced myself losses that could be avoided if greed wasn't in place.
I've had the same idea before. I've even held coins on an ad-hoc basis for people who wanted to be sure they couldn't gamble them. I was sent coins to hold on the condition that I wouldn't give them back until some date in the future.
I didn't pursue the idea further because I don't much like the idea of being in control of other people's coins. There's no upside to it unless you intend to steal them (I'm guessing this isn't a service people would be willing to pay much if anything for).
It's possible that a decent solution could be found using multi-sig addresses. For example, if you make a 2-of-2 address with the "bank", where you each control one key, the bank can simply give you their key when it's time to release the funds and you can combine the two to access your fund, but the bank isn't able to spend the coins at any point or have them stolen.
Using a system like that, you don't need a trusted escrow (in that they never have access to your coins), but you do need someone you can trust to:
a) not lose his key
b) not give you or anyone else his key until the time is up
c) give you his key when the time is up
An unscrupulous bank could wait for the time to be up and then say "I'm not giving you the key unless you pay me 50% of the coins" - in effect holding your coins hostage. They can't spend them, but they can stop you spending them until you comply with their terms.