For my part? I'm absolutely fine with one of my players having outright at-will constant flight. I've played Hackmaster plenty.
I don't mind a game with a pixie fairy flying around the entire time, bypassing traps and hazards, finding ways to aggravate enemies, and adding an additional layer of complexity to the game. It's -fun- to allow that and have that at the table. Because the REST of the party still has to get across (usually)
But from a game design standpoint it does make sense to limit things, somewhat, because of the aforementioned points.
For -my- part..? I'd have gone a different way to limiting the power of flying characters by instead:
1) Make carrying stuff really hard.
No bulky items, half carrying capacity, can only carry a willing creature of your size within your weight limit or a smaller creature that is unwilling.
Doesn't really mess up Sneaks and Casters, but we'll get to them soon. It does mean that your flying character can't swoop-n'-drop enemies as a common solution. It also means flying characters can be martial types, but probably won't be the party's pack-mule.
2) Stealth is so hard, you guys.
Disadvantage on stealth checks while flying.
Wingbeats make sound. Constant sound. You can stand still to avoid making noise but hovering still requires lift. Add on any kind of armor and equipment getting jostled by the motions... it's rough. This brings down the utility of constantly flying sneakytypes and casters since they're basically announcing where they are through big wingbeats, humming from their fairy wings, or the wooshy noises that accompany spells keeping you aloft. A flying sneakytype can still use flight to get somewhere to hide, but it's hard to stay hidden while flying.
3) Smallbois only
No medium or large flying heritages.
This alone would stop a lot of shenanigans and weirdness while also creating an expectation for flying characters. Of course a medium or large creature can cast spells that grant flight, but it wouldn't be innate. Though the above two penalties would apply to a character using flying magic.
So that means the game should design against it? I thought Level Up was advanced 5e. To me that means in part an assumption that DMs and players are interested in something deeper than WotC's version.
"Deeper" does not mean "Unbalanced"
Flight carries a lot of perks. Having some downsides to at-will flight to keep flying characters in line with characters who don't have flight while also helping to avoid Narrator overwork is not "Less Advanced" somehow.