Why not, its just a convenience thing, it would be local for each bank. What if you dont have a house and live only in NPC cities? Stuff like this just make the game more tedious for no reason... oh I love having to mail 3 sets of armor piece by piece thru the veredari, such engaging gameplay...
As Barcode mentioned above, town banks are immune to risks. Having house banks have such benefits over town banks gives more reason for people to risk stuff outside of towns.
Before the new houses this argument had a bit of weight. But I think the new system gives a perfectly good option for players to deal with such things easily.
With the new housing a player could build a armor and butcher table in their house. Next to each they could put a box.
A pve player could kill some things and place the carcasses in the box near the butcher table.
Another character could take out the carcasses at any time, butcher them and place the extracted items in the box.
An armor crafter could at anytime go to that box and get material to craft armor with. Craft armor and put it in the box next to the armor table.
Now any character that has access to that chest can come at any time and pick up any armor that they want.
All of this convenience comes with having a house now. And it is easier than ever to get one started.