There is exactly zero evidence to support your thesis, please show me where this has happen in the places where backpack funding has accorded.

Poor parents are the ones that are helped the MOST by backpack funding, rich people already send their children to better schools, no one wants to send their child to government schools, NO ONE. they all suck

They are forced to by economic circumstance and government regulation, backpack funding removes both of those obstruction

Further this idea that it would devolve into an "effective monopoly" is not backed by any data of any market, and should such a result occur it will likely be a direct result of restrictions placed on the funding by government (i.e no religious schools, no online schools, no co'ops, no education pods, no homeschooling programs, etc)

In my mind backpack funding should be a widely open to just about any educational resources not just brick and mortar schools in the local geographic region that teach the exact same curriculum as the local public schools. That would be pointless