You don't think forbidding a child to attend school is a punishment? Who is doing the forbidding - the state. Why? because little Susan might spread cancer? That last part is awfully hard to fathom.
When I divide the number of women in the USA 150,000,000 by the # of cases you cite (I rounded up to 12000), I get .008% of the population. That's not an epidemic. That's something to address through education at a kid's physicals.
But you seem more ready to give the state power over people than I am. I would set a much, much higher hurdle, and I would put the burden on the state to appeal to my reason. You would give them the power to compel right out of the gate.
You must be a nurse.
Your math is off.
The total is 11,150 plus 45,000 for a total of 56,000 per year.
56,000 avoidable hysterectomies (best case outcome) PER YEAR is not enough for you?
In 20 years, that's a MILLION hysterectomies avoided.
All because checking a box "no" is too much of an imposition on you.