Perfect bank system in my mind:
1. Universal (same bank everywhere)
2. Bank NPCs only in Capitals, preferably in a BANK house/building. - This makes the immersion way better.
3. When you visit the NPC you can view/deposit/withdraw
4. You are able to open a Bank menu from anywhere, but have only VIEW rights. ( nothing more infuriating to have to go back because you thought you have 20 number of things, when you just had 15)
5. When you open the Bank menu from step 4. you can also VIEW the items in the bank/inventary of your ALTS. (This is obviously easy to make if you have the banks/inventory linked to AccountID and not CharecterID) - this in my view is awesome QOL feature.
6. In the actual bank (NPC) you can Search for items, auto-rearange items and be able deposit/withdraw with shortcuts. SHIFT + right click - deposit all, right click - choose how many and etc.
7. In the bank you are able to expand the amount of slots you have by purchasing, same goes for Tabs. - This way everyone can have whatever suites them and strive for something. But ofc have some limit.
8. Being able to transfer stuff from one alt to another within the banking menu will be also great. Some small fee might be good to implement. This way if you are logged with Char X you can transfer whatever you wish to your alt Char Y without having to drop things on ground or mail or search for somebody to trade it to. This is basic IRL Banking functionality that I have not seen personally in any MMORPG.