I am firmly in the "it depends" camp.
You need:
a good library system
a teacher willing to learn with/ahead of the student whenever necessary
access to consumable and manipulative items for exploration/experimentation
I have access to a decent library system, that includes SOTW and a very wide selection of non-fiction, but nothing for Latin. I am comfortable teaching lots of things and, with the exception of phonics, math and Latin, the curriculum is for my convenience. However, most moms I have ask me about homeschooling are not comfortable teaching. Many end the conversation the moment they realize the state does not provide them with the plan and materials to use. So I think the temperament of the parent doing the teaching is probably the greatest determining factor for if schooling this way could work, and is probably why the early homeschool field was narrow. It is a lot easier to take off on a path that, while not well travelled, has clearly marked trails and a rough map than take off down a path that may or may not even be a path.