My thinking is not fallacious is it based on simple math.
There are about 80 million Americans enrolled in public schools.
There are about 90 thousand public schools in America.
There are about 3.5 million teachers employed, that is just teachers, the total number of Americans employed in some sort of job pertaining to public schools is probably 10+ million.
This is a system that affects about 30% of the US population, and you seem to think that replacing it with a privatized system would improve it.
There is no imperical evidence for this whatsoever.
There are plenty of articles written on this subject of how public schools are under funded, can't pay their bills, etc, etc....
There is one reason and one reason only why public schools are failing, they are not getting enough money, converting them to for profit private schools will not solve this problem.
All businesses/organizations fail for the same reason, does not matter if they are capitalist, private, public, socialist, etc. it is always lack of funding/revenue. There are plenty of private schools in the US that fail and shut down for this same reason.
No business ever in the history of economics said, oh yes our business would perform better if we got less revenue this year...
Also you keep mentioning the increase in funding for public schools, unfortunately it is not enough, simply because of population increase
https://drive.google.com/file/d/1cZso3hCgPrFgZrvVrasR1KNNIgnIV2S_/view?usp=drivesdk
Seriously... your going to have to do better than a few opinion columns related to a google search.
The data is in and it's fairly solid.
Correlation between spending more on students and enhancing performance is not existent in any real sense.
Ok... and where is your solid data that private schools are a better solution?
When schools don't have enough money to hire teachers or pay their bills that is not an opinion, that is a mathematical fact.
https://www.npr.org/2016/04/18/474256366/why-americas-schools-have-a-money-problem
The schools that have better funding do a better job at teaching children, this is true both for public and private schools. You want the public school system to be more successful than it needs more funding, it really is that simple. Replacing public schools with private schools will not increase funding, it will create schools for rich and poor and the 17 million American children who live in poverty will not be able to afford any private school.