Many cheaper online banks rely on their mobile app. Your debit card will not work wirhout an in-app confirmation. There’s no web interface (“not secure enough”).
Can I switch banks and make my life less convenient? Sure. Would I do it just to stick it to google? No.
My first thought was that a hard-fork of AOSP would be a much better solution than a Linux phone. But when you have locked down hardware, it doesn’t matter, because you simply can’t install it.
I still think a community fork of AOSP would be more efficient than Linux mobile.