Are flying characters just... like that?

Hey guys, I'm a fairly experienced player who started DMing my first campaign a few months ago, and it's been going (dare I say?) Fantastically?

A new player joined my campaign a few weeks ago and is playing an Owlkin. Which I felt would be totally fine and, for the most part, has been. However, I'm running in to a new problem in writing parts of the campaign with a flying party member.

I'm finding a common issue coming up where I feel I've written an encounter, designed a dungeon, or created a puzzle or obstacle that I am very pleased with only to remember afterwards that one of my players can fly. This often just trivializes or instantly solves some of my ideas.

For example, I was thinking of including an encounter at the end of my dungeon that would involve colored floor tiles that would activate as traps based on what the boss enemy in the room does. This would be fun to play around for my Half Orc, Human, and Tabaxi players, but what's stopping the Owlkin from simply flying the whole time?

I don't want to make the player feel like I'm pulling random ways to prevent their flight or creating encounters that are built around countering a flying character. For example, just saying "The tiles activate on anything that's in its square, touching it or not" or "the enemy sweeps your leg to knock you prone, here is an ornithological article explaining how you can't restabilize mid air based on Owl flight speed and anatomy"

I also don't want to ask the player to not fly, since it's part of their kit, and I especially don't want to ask them to change just so I don't have to deal with flight.

Looking for opinions, tips, or advice on how to create campaign content that's not semi-ruined by flying characters. Also wondering if other DMs like playing with flying races? Am I just a dunderhead? Please and Thanks :)

Edit: Wow! This is the most feedback I've ever gotten, and my first awards as well, thanks a bunch everyone!

It has come to my attention that Owlkin may be a little unbalanced as a UA race. However, I genuinely do not believe the player picked them to attempt to powergame. They, really simply, like owls.