In Australia, there’s POLi Payments, now owned by Australia Post, which gets you to enter your bank username and password, then impersonates you (https://www.polipayments.com/Security is their statement about it, and a substantial fraction of the text on that page is just flat-out lies). Naturally, doing so is entirely against the ToS of all the banks (including you now being liable for literally anything), and a few banks have publicly said “don’t use that” or similar, but they evidently tacitly support it, because I don’t imagine it would be hard for them to block.

I was incredulous when I first tried to use POLi Payments and realised how it worked—I ran away screaming, naturally. That entire business should be shut down with prejudice.