Public schools have been doing this for decades. Creating at least one good school for high intellect students. They are called magnet, governor's school, or experimental school. Where it is hoped the teaching methods tried there can be passed into the broader public school system.

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.