In this question, it's explained that Harry's hair magically remains in a similar state. It can regrow at an extraordinary pace... but what happens if Harry wants, say, a mowhawk? Or grow his hair long for a Triwizard tournament-?
This is reflected in the action figure of Harry... (showing this isn't a mistake in the film).
Now, granted, this detail isn't mentioned in the books, but what is mentioned is: Neither Mrs Weasley or Aunt Petunia can alter Harry's hair- it regrows when Petunia tries to cut it:
Aunt Petunia [...] cut his hair [...]. Next morning, however, he had gotten up to find his hair exactly as it had been before Aunt Petunia had sheared it off. Harry Potter and the Sorcerer's Stone, chapter 2, "The Boy Who Lived"
And even before Harry's important hearing, it remains stubbornly untameable...
Mrs. Weasley was attacking his hair with a wet comb. She pressed hard on the top of his head. “Doesn’t it ever lie flat?” she said desperately. Harry shook his head. Harry Potter and the Order of the Phoenix, chapter 7, "The Ministry of Magic"
And Harry apparently can't brush it either:
“He raised his hand automatically and tried to make his hair lie flat. “You’re fighting a losing battle there, dear,” said his mirror in a wheezy voice.” ― J.K. Rowling, Harry Potter and the Prisoner of Azkaban
So, what does mista Potta ever do when he wants his hair to look nice?