Mostly, charter schools select for the best students by, even if no other filters apply, selecting the students whose parents are engaged enough to select a non-default school.
There are mounds of evidence that “good schools” in the US—whether traditional private, traditional public, public-subsidized private charter, or public charter—are a product of getting the right student population rather than substantive differences between schools.
> Because the public system is largely underfunded/broken.
That's really not the problem.
The problem is that American society is largely broken, and we expect the public schools to perform as if it weren't (or to magically make up for it.)
OTOH, the schools are an easy scapegoat and distraction, and because the problem isn't fundamentally there, there is no risk that changes there will ever relieve the outcome problems enough for it to stop being a useful distraction.
I think a lot of this comes down to the metrics used for gauging good schools. Which are usually test scores, graduation rates, and discipline rates.
Assuming that the test scores measure something worthwile, test scores is always reported as a point in time measurement -- but really a progression would be more informative. What I really want to know is will my kid go up or down or stay the same in test scores if they attend school X, it's not super important what the average score is ; especially since the progression may vary significantly based on the input score.
Graduation rates could be low because of many factors outside of school, or could be high because the standards are low, and are often reported only at the high school level but kids who don't graduate high school were often not well prepared at other levels, etc.
Discipline rates can be meaningful, but if one school doesn't expel anybody because all the children are angels, and one school doesn't expel anybody because they haven't noticed the large numbers of murders during recess, the numbers look the same.
I think any town not named Sunnydale would notice the dwindling class sizes in the latter case.
Sunnydale noticed it, too.
Charter schools do not share that motivation. If they find a teaching method that works better their objective is not to share to but instead use it to capitalize and enrich themselves.
Finally, charter schools are publicly funded. If they are taking tax-payer money the results should absolutely be replicable.
If I am taking the good teachers from the other schools, I am not fixing anything, I am just transferring social capital from someone else kids to mine.
Sometimes charter schools are there to do exactly what's been described there: create at least one good school. Because the public system is largely underfunded/broken. To defy this impulse because it isn't replicable, is to deny the part the govt plays in creating the broken public schools.