It is not required that you use a CRS on the aircraft, but the FAA, AAP and most major airlines recommend using one for children under 40lbs on the aircraft.
We have always booked a seat for our children and used a CRS until they no longer needed one. You will need the CRS for the trip to the aiport as well as "most likely" traveling while at your destination anyway.
Be sure that your CRS is approved for aircraft travel, most newer ones are and will have a sticker on the back of the seat indicating this. Most CRS's will fit on the aircraft except possibly the very largest - a couple verisons by Britax etc.
In addition to the safety issue, since children are already familiar with a carseat and understand they must stay seated in one, most do much better with the carseat even on the aircraft.
I never really found it a hassle to carry a CRS through the airport. You can get a carseat duffle at BRU or Wallmart, some can be worn on the back and some can be rolled.
Most major airlines have a specific section of the website set up for travel with children.
HTH
TJ