I know a child with curly hair who's mum has agreed to straighten it 2 or 3 times as little girl wants to see what she looks like with it "long", when curly it takes a long time to get length as its coiled up.
I also know many people who've straightened hair an odd time to kill lice, this is a very well known strategy.
Tbh though its difficult if you have a child with hair that is naturally quite messy.
My child has hair with a bit of wave but not even at all and she sleeps really funny on it. If I don't blow dry it etc she just looks really messy, one side will be sticking out, the other mostly straight etc. It almost looks like it hasn't been brushed.
Children do learn from quite young that its socially expected sometimes, to try and look a bit special eg for a party. In our house we don't focus on "pretty" etc but we do say neat and tidy etc, and I can well believe DD will ask me to straighten hers to look a bit neater by age 6.
It isn't just girls either. DS hair is similar and he requested a cut recently when even he could see it was looking messy.
I dont think there's anything wrong with a school aged child having learned that it's nice to look neat and tidy or make a bit of effort to look special for a celebration or party, and it doesnt have to be in a really conforming way either.