I generally don’t have a problem with flying characters. It is as much of a problem as a benefit.
Flying inside is just impractical or downright dangerous (checks and saves). Seriously. Ever see a parakeet flying in a cage or even inside a living room?
The main issue I hear about with flying is being able to stay out of reach of melee and make combat a breeze. But to me that is just a lack of imagination from the GM.
In the air you don’t have cover from arrows or spells, and unless you are zooming around like a startled pheasant, you are easy pickings, and even those get shot too. Then there’s the added bonus of falling damage when you not only get hit, but also drop out of the sky.
Players have plenty of ways to deal with flying enemies. The enemies should apply the same methods.
Then there’s the whole issue with chasms, rope bridges and climbing. I think I can count on one hand the number of times in 30 years of gaming where I used those things as an important obstacle. And every time involved a wizard with levitation or fly. So… don’t worry about it. Let the players feel clever for flying a rope across for the others to cross, because even though you can fly, you can’t carry anything larger than a halfling. That’s why birds of prey don’t eat dogs. Just too big to carry. And so is that plate wearing half ogre.
If you’ve ever seen an eagle snap a smaller bird in mid air, imagine what that would look like with an avian character and a dragon. Yum, feathers!
My advice, don’t sweat it. If the player starts looking for ways to abuse it, then introduce a pack of kobolds with harpoons and a craving for PC buffalo wings. Getting your wings chopped off, dipped in BBQ sauce and eaten by kobolds will get the point across.