In a world where the efforts of parents don't help their kids, parents won't make efforts. This will degrade the educational attainment of all kids. Most people consider this to be a bad thing.

"diminishing the effect outsized parental involvement can have on college admissions" != "efforts of parents don't help their kids"

That really depends on how much diminishing you do. Either way, at the margin, you decrease the return to parental investment. At the margin, parents will invest less.

I don't think you can ever eliminate that, short of removing kids from their parents Plato's Republic style.

Adding more rules will just create perverse incentives (e.g. parents incentivized to increase crime rate in their neighborhoods to boost their children's scores.)

I agree that you can’t equality of opportunity without the government taking over the task of raising children. But that undermines OP’s premise. If “equality of opportunity” is not an option, then “equality of outcome” should be on the table.

I really don't like where you are going with this. It is too close to an anti-intellectualism theory for my comfort.