Is there a way to force public schools to be as good as private schools are apparently forced to be?

I wonder if I would send my child to private school if I could easily afford to do so. And I bring it up because, for the parents who can afford it in America today, private school is where they (for the most part) are generally sending their kids.

Even if the local public school is good.

And why? Because if the local public school is good, I am assuming the private school is forced to be better if they are going to be able to charge the crazy fees that they do. And if the local public school is not so good, then the choice becomes even that much more clear cut for the well-to-do parent, doesn't it?

See, right now I send my kid to a private pre-school. But that's because there is no public pre-school option (ah, the short-sighted shame of this in California). And this week, I had a mandatory parent's "before school even starts" conference, discussed a host of personal things about my child with 2 teachers as well as the school's director during a 45 minute no kids allowed meeting and walked away feeling great about the school, the educators, the class size and the overall decision to put my child in this pre-school.

I imagine for the parents that are shelling out the approximate $30,000 per year for private school at the K-12 level (that's the average cost out where I am -- and some parents have 2 and 3 kids in these schools... but pre-school is not nearly that much, though it's certainly expensive) they leave the parent/teacher meetings feeling pretty much the same way I did today. And I liked this feeling. I want this feeling. I think I need this feeling. I mean what parent doesn't want to feel as if their kid is not going to be getting the best of which that can be begged, borrowed and/or stolen?

This sentiment is certainly what drives so many people to immigrate illegally to the United States (i.e. a better opportunity for their children in the Land of the Free).

Is it a true statement to say that while public schools can be good, private schools are forced to be good or else they will cease to exist?

And is there a way to force public schools to be as good as private schools are apparently forced to be?