Teaching under Teach for America is a 2-year volunteer gig with unsustainably long hours.
If the unions were to disappear tomorrow I just don't think you'd be able to generate enough enthusiastic effective young people at that burn rate to fill out the entire system.
In many suburban schools, it's actually pretty easy for a group of involved parents to pressure the district to not renew the next year's contract of a new teacher they don't like, as long as it's done before the teacher is tenured (~three years in my state). Maybe this is one reason schools without a critical mass of involved parents suffer under the current system.