Your primary duty is to your child. I promise you, responsible parents agonize about the best options for their children. Sometimes private, sometimes public.
We started private and then left. The early years at private were probably worthwhile. I tell myself that. They were expensive.
But we've been delighted with the quality of our public schools. They operate from one third the budget of the private school (per pupil). The buildings and landscaping are dramatically tougher, but we're happy with the change. The teachers have been high quality, highly dedicated to the job and responsive to us. My kids are engaged and enjoy their schools.
You have essentially no control over the private school or the public school. In both cases, you will monitor your kids' work, talk regularly to their teachers, meet their friends and their friends' parents. Your recourse in both cases is to find a different school.
No one should demonize a parent for trying to do the best they can for their child. Your first duty is to your child. Social welfare and activism should come after family.