This is the one I'd be worried about. Thought it was annoying to not be able to use banking apps on a rooted Android? Think about how annoying it will be when you can't do much of anything, even on the Web, unless it's from a sealed, signed Apple/Google/Microsoft image-based OS...
I realize the way Firefox's user share is going, it might not matter or they might feel they don't have a choice but I really, really hope Mozilla doesn't even remotely consider implementing this.
Online fraud and theft is exploding right now and the average person is simply not capable of securing a laptop so the companies have decided to only allow secure access through a phone which can usually be trusted to be malware free.
It has to stop somewhere. 100% security may reduce the banks' fraud costs but it isn't acceptable for personal freedom. "Choose a different bank then" only works until all they all adopt it.