e.g. Banks are buying each other up all the time. After a few dozen acquisitions you end up with a giant hodgepodge of diverse systems not designed to work together, but need to integrate them. Username and password is common to all, so you wind up with raw dumps to synchronize credentials. (That's less common now that most vendors have adopted better practices like password hashing, etc. but it wasn't so uncommon back in my day)

I'm not surprised at the character limits. It simply means there's at least one legacy system somewhere that can't accommodate more. It's not necessarily tied to a plaintext database field as Troy suggests; it could simply be a validation in some line of custom reporting code a programmer put in two decades ago based on ancient requirements devised long before current-day practices. Or more simply, bank IT themselves may be unsure what their real limit is at a given point in time, and chose to go with something "safe".

I'm not denying banks need to step up their game, after all it's nearly 2020. But personally I think the reason it won't matter is most of them won't be around long enough - they're in for a world of painful disruption from the likes of Stripe, Apple, Google, cryptocurrencies, Libra-like instruments, peer-to-peer services and micropayments, etc. and who-knows-what other big innovations about to be invented by geniuses from areas of the world presently starved for financial services.