If you put that much trust in users you are in for a rough time. You’d get tons of “forgot password” requests because people expect to fill in every password field they’re presented with. If you ask them what mode of auth they used, they don’t know. Heck, I consider myself fairly on top of things, and I don’t always remember how I authenticated to some site I rarely visit.
Most users would rather wait for an extra page load than deal with any of the above.