You don’t understand the problem.
Parents who have enough education, acumen, resources, connections, etc. to get their kids into the best school possible are already doing that. What we want, for the long term benefit of our nation (and the individual benefit of each child), is for the children whose parents cannot or will not do everything possible to help them succeed in school to still be able to go to decent schools.
For example, I live in one of the poorest neighborhoods in Chicago. My last address was in the catchment area of the highest rated (at the time) public grade school in the area. At least 5 other families “lived” at my address. Got their mail all the time. Talking with my neighbors, I learned this was a common phenomenon. Any parent WHO UNDERSTOOD THE SYSTEM and had no other way to get their kid into the least-bad school in our area of the south side would pretend to live at a local address. If they didn’t get away with it, no harm no foul, because the public school system would still be legally required to take the student somewhere; but the reality is that the state of bureaucracy is such that this trick often does work.
These kids have parents who understand that getting into a good school is key, and are willing to do what it takes to enable that to happen. Thus, they’ve got an advantage in life over the other kids in their neighborhood whose parents don’t care, or don’t speak English, or don’t have a way to get them daily to a school that isn’t close by, etc.
This is why public tax money needs to stay within one system, the public school system, and used to make EVERY child get at minimum a decent basic education. Private money can set up any school they want. Charter schools don’t have to be supported by the government, especially not to the detriment of actual government-supported education.