Problem is that banks place a lot of trust on a locked-down phone and I have a hard time trusting a blackbox device I don't really own but only paid for.

That's the reason I mostly use online banking on the web, not on a device.

If it ever comes to that in my country I can also use my previous, unrooted backup phone to host these apps and keep it at home.

I'm not at all thrilled of the idea of carrying your credentials to your bank account on your phone, accessible via a 4-digit PIN out there in the world in the first place. For some reason, banks think it's great.