Do not think your analysis proves true in practice. Schools will lose students and money if student numbers go up and excellence subsides.
Public schools don’t lose students under the same scenario.
When you have a private school you have to produce an excellent education as in any private business to retain students(customers).
A government monopoly like government public schools don't have any competition and won't lose students even though too many of them produce the worst most unimaginable products and services imaginable.
A private business has to produce a excellent quality product , efficiently , at a great value to remain in business today. And they have to do it better than all competitors in a free market. Government Regulations just limit competitors that can't meet those regulations so it lessens competition.
Blackberry produced an excellent cell phone and had 40% of the market .But along came Apple and Steve Jobs with the iphone which destroyed Blackberry, Nokia etc and so now iphone has 50%of the market because the iphone was superior product . this is why competition is key in producing excellent products. Now ihpone and android are in competition .
For example there are these private coding boot camp schools now And they pop up because government schools and , government regulated colleges don't teach the iT tech skills businesses need. But still these coding schools re not really free market businesses as they give government backed school loans etc.
sO if we remove these government regulations like the school loans etc we would get closer to real free market principles. compare the invovation in smart phones especially android phones now . It's because there is less regulation in those industries that there is more innovation, lowering of costs and improving of quality.
Education is a a service just like any other as these 33 private coding boot camp schools show
At the moment, the balance is still very uneven. The masses send their kids to public school. The more attentive, involved, educated parents send their kids to private school, and a few of the less fortunate find ways to get their kids in too, and those few kids benefit BECAUSE they are few.
If the situation changes such that all parents can use vouchers to switch over to private schools, the private schools will have essentially BECOME public schools, and as such, the quality of students will... change (I'll put that delicately.)
Now, any private school that resists the lure of easy money and upholds the standards for enrolling and expelling will be okay... it's just that from what I have seen here in LA, they can't resist. Suddenly, all this money comes rolling in if you accept these "other" students.
And here's an extra grim warning: women with problem boys (usually single moms) that have been kicked out of several schools are particularly drawn to private schools. Just letting you know.