I also don't remember there being banks in Elder Scrolls games. Let me guess, you couldn't connect the dots to come to the logical conclusion that houses would act as your bank? Even the lowest level character could rent a room out with a single chest and some modest ways to decorate. Everyone would have access to their bank without breaking the lore of the single player games.
There were banks in Daggerfall, but those were actual banks, not some sort of global safety deposit box. You could get loans, get a letter of credit, cash in letters of credit (merchants paid you with a letter of credit if transactions with them went beyond a certain gold value), and store money. You could also buy houses and boats.
Let's say each server houses 10,000 players. Are you going to include 10,000 homes in each major city? How many available homes are you going to put in the wilderness? How many homes are you going to put in smaller towns that are available? Do you protect player homes from being broken in to? How? How do you prevent players from using cheats to get into homes? How do you inform a player if they have been robbed, if you even inform them at all? How do you prevent other players from not littering player's houses with items? How about preventing them from stacking corpses in your house? Is every house of the 10,000+ going to look exactly the same? Will they all have the exact same upgrades? Etc, etc.
All of those are rather easy to deal with:
Where are you going to put Homes: It's rather easy to designate certain areas as being off-limits to player-built homes, so the devs could define certain areas of open terrain as areas where players could build, and players could only put homes in those places. Another possibility would be to have have multiple homes throughout the gameworld with instanced interiors. Players "buy" their own instance of the interior.
Do you protect players homes from robbery? How?: This one is insanely simple to deal with. You simply program things so that only the person who has rights to the interior can place or take objects. Galaxies did this quite easily. Even if someone glitched into a private home somehow, they could never rob the place. The game simply wouldn't let someone without the proper rights take objects.
Other players placing items in the house: simply disable the command for dropping items when inside another person's house.
Corpses: We're probably not going to be able to drag corpses in this game, so it wouldn't really be a problem. Especially if interiors are instanced. Even if someone lured a monster into the house, the house can be set to not allow most players inside. Even if a player glitches themselves inside, the monster probably can't do the same.