"flying" is an 'evergreen' mechanic in magic the gathering, which means it's been used in every single expansion in the 30 years since the game came out, from 1993 to the present day.
flying is commonly cited by mark rosewater, the game's head designer, as the game's best mechanic in part because it's so intuitive: flying creatures can't be blocked by creatures without flying¹. it's elegant and crucially it's memorable. it instantly 'makes sense'. you hear that and think 'oh, they just fly over the other creatures, okay'. very few players misunderstand flying. and even better, the art of the game helps to reinforce that. almost every flying creature ever printed is shown either actively flying/levitating or with huge conspicuous wings. remove the text from cards and ask players to tell you which creatures have flying and they'd get it right 99% of the time.
in fact, the biggest reason why anyone ever has a problem with flying is that the art being such a reliable tell means it can also mislead them: breaching hippocamp got a few players confused because the art makes it look like it flies. rosewater considers whippoorwill's art to be a mistake because it confused players by straight up depicting a winged bird flying on a card without it:
so, you know, the rigid art/flavor-mechanics divide would hold that these are just cases of players being mistaken, of not understanding the mechanics of the card. but as anyone who has tried to write rules text for anything will tell you, if your rules text is consistently misread in the same way, you're doing something wrong! the players who played as though breaching hippocamp and whippoorwill had flying had their mechanical experience severely impacted by the art!
and those edge cases aside, the fact that flying is usually so conceptually intuitive and easy to convey with art makes a huge difference to the mechanical design of cards! a card with a more complicated keyword like ninjutsu, undying, wither or evolve loses a lot of the space it has allocated for complexity. flying, however, uses almost none of the mental bandwidth that goes into understanding a card, and this has an extremely tangible impact on what kind of cards can get flying compared to those other keywords! if you can rely on the art and in some cases the creature type (birds, dragons, angels) to make the 'flying' on the card 'stick' in a players' head, you don't need to worry about how it contributes to the overall memory and complexity issues that card might pose.
& none of these things would be true--i.e. the 'mechanics and gameplay' of the game would be substantially different--if flying were just called "Untitled Ability Keyword #1"
¹or reach, but that's besides the point right now