Not necessarily. Charter schools do much better if you measure just output, but are frequently quite average once you control for their advantageous population.
It depends how much you weigh “Does the charter school actually teach my child better than a public school”(statistically, no, and they might even teach worse!) and also “do I care about exposing my child to people they’re different from”(ie. Avoiding them being stuck in a bubble) and also “am I unable to find another environment for intellectual pursuits”(clubs, extracurriculars, etc. when I was young there were definitely after-school schooling available for smart kids, and at school you can stay late for science teachers to teach you more science).
An individual parent’s incentives do tend to point in this direction, if their metric for success as a parent doesn’t include being exposed to children whose family’s aren’t as successful.
But when taken to an extreme, this leads to exclusive areas and excluded people.