> School choice means competition among schools. Which leads to winner and losers.

This doesn't follow at all. Consider e.g. a company that sells different flavors of spaghetti sauce (https://www.ted.com/talks/malcolm_gladwell_on_spaghetti_sauc...). The flavors are competing, but only on a per-person basis; overall the flavors are optimized to satisfy everyone's (different) preferences.

It's quite easy to imagine a similar concept in education, where people learn better from a particular teaching style or are better served by a particular curriculum. There's no obvious reason to expect that one "good" school would be sufficient for everyone's needs; the ideal situation would instead be that one could choose from several schools, of which at least one is "good".