Can a parent decide that a child needs a day off without a doctors note?

I can write a note for my daughter if she misses school. It doesn’t have to come from a doctor.

Yes. Schools don’t require a note from a doctor until the third consecutive missed day.

When my daughter was in school I called her in “sick” on plenty of occasions over the years when she was over tired, under the weather with allergies r simply needed a day off. I don’t know how the system works now, 20 years later but unless the absence was a week or more, no doctors note was ever required.

Sure.

Where I live, we can be out for days and there’s no requirement for a doctor’s note. They ask that you call in and if you don’t, they call you.

Yes, of course.

Unless I was vomiting or had chickenpox. I went to school. It was considered out of the question to miss even one day.
I’m sure my parents could have kept me home if they thought it was warranted.