Back in the day bank feeds were horrific to develop but these days I think there are aggregate feed services. Seems like you could just implement support for one of those?
There are some things that are “natural SaaS” and interoperability with ugly services run by huge banks that are probably moving targets and probably have administrative overhead to use is one example.
Plaid offers transactions APIs (https://plaid.com/products/transactions/), but I guess to your point these APIs are geared towards fintech companies, not personal use.
EDIT: I don't know how well it works in general, though. You'd have to test it yourself.
[1] https://github.com/simplefin/simplefin.github.com/issues/14