When I stop past the while line, it's almost always because I thought the way was clear, but then something happened, and I had to stop, and then the light changed, and I was stuck past the white line.
If you implement your plan I would never even see the light become red!
Do you drive much in cities? I'll lay out something that happens all the time:
I cross the line slowly, and some pedestrian darts out, so I stop, by the time they cross, the opposing traffic has a green, I however (in your scenario) do not know this because I can't see that the light is red for me.
So now I'm driving forward, thinking I'm good and some car comes flying through because it's green for them, and they can't see me because of the layout of the block.
I need to see and know that the light is red and just stop and wait there.
Similar things happen when the car in front of me wants to turn left, but didn't bother with a blinker - I'm in the intersection, past the line, and suddenly I need to stop because he's turning. He turned, but now it's red for me and I better wait right there, and not go forward, because other cars are about to drive.
You also aren't taking into account the varying heights of cars. If I'm in car behind a van, I won't be able to see the light because it's directly above the van so I can't see it.
Also:
Your goal is to keep cars from going too far into the intersection after a red, right?
The problem is you are assuming this happens due to incompetence, but it actually happens because of driving conditions like I mentioned.
And that's fine, because you've _already crossed the line_ and therefore you can (and should) go through. You're no longer running a red light at this point, since it's behind you, you're just crossing the intersection like normal.