Also, unlike your other examples of strangers working on things, there's not really a feedback loop of review and rework where mistakes can be corrected. If your child gets a bad education, that's time lost that's really hard to recover and can set them back for life.

Edit: To add, the "ideological capture" perception is important because of what education is. When you're dealing with an electrician, it doesn't matter who they vote for because electricity works the same way regardless. Teachers don't just regurgitate information but promote a set of values and expectations in their classroom so their personal opinions can matter a lot. And that's not even getting into teachers who explicitly try to teach students their worldview.

If the water you drink is having problems, you'd have campaigns over it, protests, people trying to get it resolved and potentially lawsuits. People would band together to do whatever they could to fix the problem that they see.

Education is seeing the exact same thing. Parents see a lot of problems. They are going to school board and council meetings, people are campaigning on solving the issue and people are taking whatever measures are in their power to fix it...like home schooling.

When people see problems, they want to fix them. It's exactly the same thing.

I have some friends who live in area with the bad water quality... They end up drinking/cooking with store-bought water, instead of city-provided one from the tap.

When I need electrician/plumber/general contractor/etc..., I choose one based on recommendations and reviews.

If you know (say from conversations with other parents) that your local school is bad, why would you send your kids there? It is like choosing an electrician with bad reviews only because their office is next door to you, or living in bad-water area, drinking city water and getting sick every week.

Schools are limited for choice, expert evaluation is limited, outcomes are potentially unclear... That's before you get into issues with the politics of a teacher or problem students.

Education is massively different. It's not a simple one-off deliverable, like making sure wires are insulated or water is filtered. It's something that's has different success criteria for each person who consumes it. It overlaps significantly with normative considerations and subjective values. And the current infrastructure that provides it via public institutions is badly distorted by perverse incentives, ulterior motives, and dysfunctional mechanisms of accountability.