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Your question quickly progressed from polite inquiry to decidedly confrontational and personal. I kind of loved it. :) I'm sorry about what happened to your sister's disabled kids.

The general reason parents can confidently provide primary education is that a) good educational materials are easy to research and acquire, b) the benefit of education closely tailored to a child's strengths and weaknesses meets or exceeds the benefit of institutional pedagogical theory and classroom management skills.

In secondary education years, access to material and closely meeting needs still factors, but the parents' operating principle is increasingly about pulling in the best sources available. That often means community college or part-time high school classes.

There are also a lot of homeschool co-ops, pods, and other resource and skill-sharing arrangements. Lots of variety.

All your examples of authority figures are trained to be effective over a high volume of lower trust interactions with the general population, relying on professional incentives to perform. They are needed but they're most effective when complementing and backing up parents who cannot for whatever reason provide care, correction and education at home.