Why didn't Harry summon his broom to fly over the maze in the Triwizard Tournament?

Probably because he was not allowed to

"We seemply ’ave to get through the maze?” said Fleur.

“There will be obstacles,” said Bagman happily, bouncing on the balls of his feet. “Hagrid is providing a number of creatures . . . then there will be spells that must be broken . . . all that sort of thing, you know. Now, the champions who are leading on points will get a head start into the maze.” Bagman grinned at Harry and Cedric. “Then Mr. Krum will enter . . . then Miss Delacour. But you’ll all be in with a fighting chance, depending how well you get past the obstacles. Should be fun, eh?”

—Harry Potter and the Goblet of Fire

When Fleur asks Bagman whether the champions must get through the maze, Bagman implicitly replies in the affirmative. He then mentions a number of barriers that champions must overcome. It is not unreasonable for the champions (and the reader) to conclude that the maze must be navigated on foot.

If Harry (or any other champion) had summoned a broom, let alone flown over the maze, they would have been noticed and presumably disqualified.