Scrap helmets and pads, improve safety and technique
I understand the idea you have and the process behind it that leads you to your conclusions.
I'll just say that this tree you're barking up is the wrong one.
Football is violent, period. And it's not just the violence, it's the depth of it. Virtually every single move in the sport is fraught with violence. Not potential violence, but violence. I know people don't like the comparison with the gladiators but that's pretty much what we've got. Modernized coliseums and modernized gladiators battling for physical supremacy instead of death.
We don't LIKE to see injuries but we still know they're going to happen and so do the participants. It's an understood quantity.
Taking the pads off is not going to stop a 280lb DE from crashing into a 210lb QB at full tilt. It 'may' make him turn his head to the side before impact but the impact will be just as forceful and without the padding would be much more likely to produce some form of injury. So even if you get the head injuries down you're bound to see more broken bones, torn ligaments, contusions, lost teeth and bruised muscles than ever conceived.
What I can envision from your scenario is a season that might only last 8 or 10 games before there weren't enough players left to actually have a game.