First of all, Stanford's CREDO study:
The study reveals that a decent fraction of charter schools, 17 percent, provide superior education opportunities for their students. Nearly half of the charter schools nationwide have results that are no different from the local public school options and over a third, 37 percent, deliver learning results that are significantly worse than their student would have realized had they remained in traditional public schools. These findings underlie the parallel findings of significant state‐by‐state differences in charter school performance and in the national aggregate performance of charter schools.
The US Department of Education's study (middle schools only):
On average, charter middle schools that hold lotteries are neither more nor less successful than traditional public schools in improving student achievement, behavior, and school progress.
A Rand study is also a "mixed" review, showing that there is some good and some bad in charters:
Charter schools in most locales have marginally greater variation in performance than TPSs [Traditional Public Schools], as measured by the achievement-impact estimate for each school, and, in some locations, this may simply reflect greater measurement error associated with the smaller average size of charter schools.Even the KIPP schools, which I first heard about from Outliers (great book, btw) and greatly admire(d?), have some doubts. It appears that some of their success is from "selective attrition", as evidenced here and here. There seems to be this idea that if we just privatize education (or anything), that the magical free market fairy will make everything right. (Ignoring that privatization can debase things, one of which is education.) But this just seems to be the way the world works now--ideology trumps reality. If the reality isn't reflecting ones' political view, well, obviously, the problem is your idea just hasn't been given a fair shot--it certainly isn't that you're just wrong.
How Charter Schools Choose Desirable Students.