Elementary school kids can miss a day of school. If they are doing something wholesome and constructive on their day off, no one would claim that it hurts the child who is doing the alternate activity.
Does it hurt other people? There is an ungated section of this Matt Yglesias post concluding that when rich people pull their kids out of school it “… ultimately harms less-privileged children.” For now, assume that is true. We could internalize the externality, like surge pricing on toll roads. Let parents pay a fine to take their kids out of school. The fine would fund programs that help everyone. Let parents pay back into the public good. Charge $25/day which could go toward buying classroom supplies for the inconvenienced teacher.
This flexibility might lead to richer families keeping their kids in conventional schools, which seems like a good thing. No one would have to pay the fine. There is and would still be a system for excusing absences due to unavoidable things like surgery.
Requiring a doctor’s note for excused absences is already a tax. Requiring a parent to miss half a day of work to go take a child to the doctor is more punishing than paying a $25 fine, for many families.
The fine could even increase with the number of missed days. Only super rich families would be able to afford to take 2 children on a 3-week trip. I wouldn’t be able to afford it. But I wouldn’t mind if our school generated revenue off of those who can. Those people would probably donate a new playground in exchange for a plaque.
Is another example where it would be reasonable to charge people to not use something? In a way, insurance companies try to fine people for not using the gym. Running with this example, paid private schools could easily call this a tuition reimbursement for high attendance. Unfortunately, I think it would be politically impossible to implement in public schools.
Economist Writing Every Day 
A reimbursement for attendance is a way better look, and more palatable politically. That’s not a terrible idea at all.
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Just a lot more expensive. Providing schooling free of charge to the user is already a big subsidy.
Forcing people to attend is a severe restriction of their freedom of movement. Paying them to attend is better than that. But who’s going to pay for all that?
Separating school and state would be the way to go. Just many places already separate church and state.
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I hear you.
I send my kids to private school, so it really would be a reimbursement, and much more consensual – even with vouchers. It would test the legal limits of vouchers, even though it’s not a problem for school choice in principle.
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What about homeschooling?
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Homeschooling would allow you to travel with your kids. I understand why some families make that choice. Personally, I really value being able to send my kids to school. If the school won’t let me travel as much with my kids, then I just won’t do the travel.
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Birmingham, AL will now offer payments to families in exchange for good attendance. “Birmingham City Schools to launch Every Day Counts initiative” https://www.cbs42.com/news/local/birmingham-city-schools-to-launch-everyday-counts-initiative/ “Similar to Birmingham Mayor Woodfin, they say truancy within the district is a big concern that requires action, as the district previously reported that 25% of students are chronically absent.”
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