Well you're partially right. After all, the "big tech approved phone OS" is actually Linux, so just having a free OS isn't enough to prevent it from being co-opted and turned into a locked-down platform.

But the partially wrong part is, we can make our own platform. PCs let you install and run any software you want, because it's an open platform. If we make an open platform smartphone that can compete on features with the closed behemoths, and that then becomes popular enough, then banks may offer apps on that.

But this is tricky too. Linux already has issues getting official support from corporations. We'd need our open platform to be compatible with the closed ones, so that it's easy for banks to run their apps on our open platform. There are already ways around this, like virtual machines to run Android, or other methods. But the closed behemoths may try and end-run around this, like DRM. So we'll still need to advocate for our rights and compatibility.