“School choice” is just marketing language to disguise “funneling general tax dollars into private schools so wealthy people don’t have to pay for the privilege.”
No. It's about pushing decisions out to the edges and empowering parents (and students) to help run the school system. To frame it this way is to deny the powerful evolution brought about by real choice.
Wealthy people don't want more students going to their children's schools. School choice is about funneling public funds to evangelical (aka extremist) Christian churches.