In an area where everyone homeschools there should be no need for any kind of government schools. That's not the case now --- but we should go back to what the Constitution decided --- and it limited the scope of the federal government. It was never given the authority over education and should remove itself. Same with health care.
Where is this utopia to be found? At present, homeschooling is about 2% at most of the school-age population. Even with widespread awareness and more lenient state laws (compared to 20 years ago), the numbers are still comparatively small - mostly because homeschooling requires one parent to stay home.
There will still be a need for schools, because there are homeschoolers who do transition to school. One support group I belonged to for awhile had virtually no homeschoolers over 6th or 7th grade - they almost all went to middle school (or more rarely, high school) after being homeschooled as younger kids.