First Tech in the Pacific Northwest used to invent their own wheel, and it was great. Usable UI, 2FA; I had no complaints. Then they switched to what I assume is some pre-packaged SaaS. It's awful. Not even an attempt at MFA, just UID/PWD and off you go. UI sucks. Stuff doesn't work if you don't allow popups, but doesn't fail in such a way as to make root cause obvious ("here's an obscure error message with a string of hex numbers..."). I wish they'd go back to what they had.
There are a healthy assortment of fintech offerings for banking clustered in Austin and on the West Coast, maybe more.
Check out Q2 and Malauzai in Austin (there are are several, these are just the two I have evaluated) for a stack that is agnostic of the core system and provides almost all banking functions across channels.
This kind of thing isn't cheap though, and bank boards are notoriously conservative when it comes to innovation, especially for small banks.
One such is Jack Henry. I just interviewed with them (but didn't get the job, which is too bad as I really wanted to work there). They offer everything you need to start a bank or credit union, at a couple of different complexity levels.
There are definitely vendors for at least some of the backend and web services a starting bank will need. I've forgotten any of the names I've heard, though.
