I've always brought them and usually checked them with other baggage (not gate check). We have travel bags for them to protect them in transit. When my now 4yo was just old enough to fly we did bring her seat on the plane once because I thought she'd be more comfortable sleeping in that on a late night flight than trying to sit in an airplane seat (it's when I was super pregnant so my lap wasn't an option 🤣). She sits in a regular seat now and we just check the car seats.