Would be interesting if players could set up their own shops. I like the idea of game-tables and slot machines. Darkfall has player vendors (you can only sell from them, tho, as far as I am aware). It also has slot machines which are always a bit of cheap fun. Also allows for people to set up herb gardens to get reagents would be neat.
One thing Mortal has done right (and will be improving upon in their future expansion) is allowing players to set up their player vendors to sell AND buy. There was a guy who had a house near my favorite bear spawn that set up his vendor to buy 10k stacks of bear carcass for a fairly decent price. Not as much as you would get if you took it in to town and had a butcher do it there, but enough to make it worthwhile not to make the trip back to town with the carcass.
I always enjoy tools that allow people to do fun things with their houses. Imagine if a player could set up their own Inn if they buy one of the really expensive multiplayer houses, by renting out the individual rooms. Or a casino full of slot machines and other gambling games.
Mail boxes would make for an interesting thing. If you make it so stuff has to manually be put in the mail box (not some mystic system that allows for people to safely transfer stuff across different towns). Might give way to player curriers.
There's a bunch of wonderful and neat stuff that could be done with housing in theory. The real question is, what are the limitations? It's quite possible that the games engine just wouldn't support some of the stuff we would like to see. And if it could, maybe it would require more programming than it's worth (there could be other features that need to be done first).
As for a chest that links to a bank, I say no. If you do that, you take away almost all the danger of transfering items between towns. Not all towns have banks (I think?), so all you have to do to transfer items from somewhere is to buy a house there and set up one of the chest. Even if the chest was super expensive and/or a rare drop from an epic monster, it would still eventually become pretty common-place after a while. Then it would just potentially ruin a possible game play feature (ambushing caravans/travelers to steal their gear).
Of course, it could give rise to something new if it is put in. Pay someone to transfer an item for you. People would want to build up their reputation so people would hire them to transfer items using their bank-bound chest.
I'm always going to be an advocate for things that 'puts the power in to the hands of the people', though. That means sandbox features such as lots of house customization/fun. I would enjoy it if the economy was taken out of the NPCs hands and put in to the hands of the players, in all areas. I would also enjoy it if houses became more than a place to store items.
Would be neat if players could set up their own banks by buying a house of a certain size and hiring a few NPCs (a clerk/bank manager and some guards). He would gain an amount of money for each account that has money in their storage at that bank. But he would also have to pay the NPC's wages and the 90-day rent.
Damn I wish there were a game that gave all the tools to do that stuff ;(