Having multiple banking factions could create some interesting in-game interactions between the banking organisations. Competitive interest and such, and maybe even conflict between banking factions over representation at different stations, access to customers and such. Would certainly create a good opening for mercenary groups if the banking factions don't have many pvp orientated members.
Although, at least currently there's not really any reason to have a bank. Credits are linked to your account and can't be lost.
A company/faction joint account would be about the closest thing that has an actual use at this point.
Hopefully as more economy features are implemented a bank will become a more meaningful addition.