Not quite - a malicious server would receive the plaintext password in the current status quo.
Further, a fake website can sidestep this by not using a secured connection and just faking the UI.
Windows reserves CTRL + ALT + DEL for this reason, but doing that on a tablet / phone that's already in production quickly runs into issues. Also, windows had plenty of issues with fake login screens.
PS: I suspect protecting people from such things ends up requiring fairly strong AI or significant compromises.
In the end, I'd probably prefer something like SRP
Not if the server generates a unique ID for each attempt, and that ID must be used in hashing. It can be as simple as a timestamp.