It's just a very large volume of luggage to be traveling with. Two young children require an awful lot of luggage to begin with: diapers, wipes, food, changes of clothing, towels, toys, strollers, etc. And trying to keep them happy is stressful enough on its own. Add in two bulky car seats, which as I recall need to be checked at the gate so you need to bring them all the through the airport and security, and the whole experience can become downright unpleasant.

Car seats can be checked as hold baggage and claimed at baggage claim. In the US, I believe they have to be free (in any case, I never had to pay for them [nor strollers] and they never “counted” if it was just a car seat or stroller, even on Spirit).

We would generally bring the car seat onto the airline and have the child sit in the seat on the flight. It prevented some of the chaos of wanting to run around the airplane. “This is transport; just like in the car or other airplanes, you have to be in your seat.”

Needs a window seat (obvs) and the red sticker “approved for aviation use” (which the cabin crew did check every single time, which was impressive). Ask for a seatbelt extension and adjust the belt so the buckling is done on the side rather than smack in the middle of the seat.

Carrying it around, along with the other luggage. It's not exactly a convenient, portable thing.

You can use a fabric-only portable car seat.

No, not in America and not on airlines. Here those aren't a thing...

not a parent, but checking baggage is already an inconvenience. once I was old enough to pull my own suitcase, my family never checked a bag again.