Ever notice that terrible ideas can sometimes be seeds for the best ones? Consider this...
If I am right, I believe that a big advantage of this approach might be that password managers would still be able to fill in the fields in the form... and you could do it without modifying Moodle core at all.
Whether I have accessibility issues or not, it is really convenient to use a password manager to fill a form for you at the click of a button or the swipe of a finger print. I don't think this would be possible if you had a page re-load in between the two.
Let us know how your project works out or if you just want to do some brainstorming.