Why in the world do you think that standardized testing is good for, or inherent to, charter schools? Standardized testing long predates charter schools. Standardized testing -- and standardized curricula, which is what Common Core is really pushing -- are in many ways an antithesis to charter schools. Charter schools are successful to the extent that they can distinguish themselves from what their (public or private) competitors offer. If all schools have the same material and the same tests, and those mandated bits cover as much of the school year as Common Core says they must, then charter schools will have precious little to distinguish themselves with. Besides, charter schools are at best a hybrid between private and public education. They're good in that they generally let parents choose a school for their children, but bad in that they are much more accountable to the existing public-school bureaucracy rather than to parents.
The primary way that government has (very intentionally) pushed private schools to the sideline is by using fairly uniform taxes, usually in the form of property taxes, to pay for the public schools. Anyone who wants to send a child to a private school has, until the very recent phenomenon of school-choice vouchers, had to pay twice: Once for public schools, and once for the private school they choose for the child.