If you’ve entered the intersection on green or orange, and must await oncoming traffic before you can safely turn left, then the light turns red before oncoming traffic clears, once that traffic has indeed stopped for the red, you need to complete your left turn to clear the intersection, even on red.
This situation is clearly spelled out in the driving manuals for my state.
If you are not willing to continue on if the light turns red while you are in the intersection, then don’t enter the intersection until it’s clear - wait behind the line.
Other traffic (who are now, or have been) waiting at a red light should be able to tell you’re in the way and wait for you to move.
Note that I'm assuming an unprotected left turn (with right hand traffic as in the US) at a busy intersection with incoming cars running yellow lights; please let me know if any part of my assumption mismatches yours.
This also encourages drivers to actually stop in the right place (since they can't see the light otherwise), and it's friendlier for pedestrians since it avoids drivers stopping on top of the crosswalk.
(I've also never heard of the turn-right-on-red rule anywhere other than the US. Over here in Portugal if it's fine to turn right while the light is red, there's just going to be a separate green/flashing light to turn right. A lot clearer!)
We do this kind of thing in many other places in life. Imagine if we didn’t use barriers anywhere and only used painted lines to tell people where to be - don’t walk to this side of the line, that’s where the valuables are “stored” (no walls, just markings.)
We use ‘guardrails’ all over the place. Sometimes to nudge people (one can jump a literal guardrail), sometimes to prevent injury (you simply cannot physically access the active industrial robot without intentional effort), and all kinds of inconvenience in between to suggest where to be.
Place the lights so that they’re only visible further back, and people will stop further back.
If you implement your plan I would never even see the light become red!
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.
This is not a hypothetical "if", pretty much every country in Europe has traffic lights set up like this. Just take a look at Lisbon or Amsterdam in street view to see what I mean.
The major problem is that on very congested streets, the driver won't know if the exit will be free of traffic when the light turns red. Blocking the intersection is illegal.
To a certain degree, it is a failing of Civic design and the ruleset. The solution is generally no left turns during peak hours, which is a duct tape fix
This competency shortfall is present in other transportation- and infrastructure-related fields. See for example how badly North American construction companies and government bureaucracies handle big transit projects. Third-world levels of mediocrity compared to the cost-effective, competent management in, say, Spain or Japan.
A couple weeks ago, a 55mph limit near me was lowered to 50mph. A cop watched during the busy times for a few days. Now everyone is generally going 5mph slower than they were. Seems successful so far.