Why not? My dog prefers Cub flying because she can see out. I use a chest harness on her and when in a Cub I tie her in, but in my case it's the back seat. The primary reason I tie her is to control her while warming the engine since the door is open and the prop's spinning, and for loading and initially during unloading. I don't want claws mixing with fabric as she tries to exit the plane. She can't get out of a Cessna until I slide the pilot seat forward so there's no issue there.

PS. Another thumbs up for Mutt Muffs.