In the book universe, Voldemort is the only one who unlocked flying without some kind of vehicle (which a few others learned at some point, like Snape). It was more cinematic to have everybody flying around in the movies, though.

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You can get anywhere using your feet and walking. You can use your feet to pedal a bicycle. You can use your feet to work the pedals of a car. All of them can help you travel great distances. Some of them require less of your feet. Same with magic and magic items.

There’s no direct in universe explanation that I can recall. But, if you look at wands, you’ve got special materials being used to harness and control magic in a way that isn’t possible without them.

So, it would make sense that brooms would be made of similarly special materials that enhance flight, or make it easier. Which, other forms of flight do seem to be less efficient overall.

Not that the idea of magical tools is exclusive to potterverse. Pretty much every magic based fiction includes some kind of crafting or another where using magical materials does something different, or working magics on materials makes them permanently able to do something difficult to do on command.

So the broom thing makes total sense, even with other methods of flying available.