To me, the amount of criticism public schools receive is an indicator of their worthiness - people are able to inspect the education and intervene directly if they feel it is inadequate, and the government has the ability to provide useful oversight and assist in setting standards. I'm sure there are many cases where this centralization is to children's detriment, but at least it is a largely transparent system.
In comparison, the only real transparency provided into a homeschooled child's education is when they start college and have to find out whether they really learned enough essential skills and information to be able to compete in a real educational environment. If the answer is 'no', it's too late to do anything.
Objective measurements would be great, and so would more rigorous enforcement. Historically, homeschooling groups are against both.