I see a downside to it, What if its VISIBLE and one forgets to lock, that will allure many to open the door ! steal, whatever, and its very possible to have valuables in a car !

There would be no clue in the car itself wether it is open or not but in the remote-control-key-holder or whatever I have with me.

Would the remote simply display whether the lock button had been pressed recently, or would it have to receive feedback from the car indicating the condition of the locks?

No, no feedback. As to receive a feedback I should get closer to the car again. Maybe the fatal question ("did you lock the car") happens in the cinema! I only have to take the key-holder-remote-control, check it and see the last pressed button (or position of the switch) is "CLOSED".

I avoid getting nervous on my fast way back to check wether the car is closed or not.

At least on our factory remote, it has separate "lock" and "unlock" buttons, plus the trunk button.

Since I'm "old school," I never trust the remote to lock the car, anyway. I only use it to unlock.

Thanks for this great simple idea of course it would be better if the remote contrrol, while locking, will receive a signal back saying if the lock operation succeeded (e.g. if a door is slightly open - the car might fail to lock)

But - let us first have the simplest solution you raiesed.