To my knowledge, homeschooling is about 1-2% of the school age population, and I don't see it getting appreciably larger.
In reality, what people with intact families and any money at all used to do was move. First they moved out of the inner cities to the suburbs, and then from the inner suburbs way out to the "exurbs." Their exurban school districts have been largely pretty good, and many parents have been satisfied with them.
With No Child Left Behind, that is changing, because the quality of a district is *not* determined by the people who live there, who run the school district, or by the state, but is rather determined by the federal government. The federal government has for now defined about *half* the school districts in the entire country as "failing." In St. Louis, virtually *all* the St. Louis County (suburban) districts are now on the "watch list."
So it doesn't matter how far you move, anymore - as long as a district has an "identifiable sub-group" (either minority, or special education, or both), if that ISG doesn't get up to "proficient" standards, the district will be labelled "failing."
Just about every large exurban school district *will* have an ISG of special-ed students, and thus ultimately practically *every* district in the US will be considered "failing," if this nonsense continues.
People in the US by and large have shown themselves committed to public education - when they themselves have some control over it, especially in being able to buy a house in a good district.
Homeschooling has been one way for parents to control their children's education, but expecting everyone - especially parents who believe that a good public school education *is* best for their kids - to do it is unrealistic.