I disagree; fliers are a much bigger issue here because they have a wider range.
Again, they're as common and as dangerous as you want them to be.
In LU, the world is divided into regions. Most humanoid settlements are going to be in Country Shires and Urban Townships. Monsters are going to be quite rare in those regions because those regions are well-patrolled. It can also be expected there are at least a few people with classes living there, especially casters that can help defend the settlements. Even a single low-level caster can do a lot to keeping a village from being destroyed, and most D&D/LU games these days are going to have casters be a bit more common. When the monsters get to be too much, that's either when the ruler sends forces--possibly even forces on
flying mounts!--or puts out a call for adventurers to deal with the problem.
Or you take the game to its logical extreme and assume that the world is in a nearly apocalyptic state because of the presence of monsters. Which is perfectly fine and can be a lot of fun, but is not, as you put it, a typical fantasy world.
Plus, there's also plenty of other things you can use. People use scarecrows to, well, scare off crows. In LU, scarecrows are constructs. What if their actual purpose is to scare off flying monsters? They don't
need to be "animated by the echo of a malign spirit," after all. Voila! You have a nice little guardian for your farms. Or take a bit of history and make it a law that your peasantry are forced by law to practice the bow. That may even be a bonus proficiency in some of the Cultures; can't remember off-hand.
And this whole thing isn't even nearly as big a deal as you're making it out to be, since your intelligent monsters can use ranged attacks and, even if you limit flying PCs to three consecutive rounds of flying as per the current rules, they will still be out of melee range most of the time! If that
actually is screwing with your encounters--and I'm
pretty sure you don't actually have that many examples from your own real game of it messing things up--
then you can alter your encounters to deal with it.
And you don't even have to allow flying PCs in your game in the first place. Limit your table's heritages as much as you want. My upcoming game has only four PC heritages!