Children under 2 can fly free on a parents lap, but my wife insists on buying our 4month old his own seat for safety reasons. There will be zero chance I talk her out of this now.
Its basically the difference between seat belts that work, and seat belts that don't work. There's plenty of space in between perfect landings and crashes that kill everyone onboard. Seat belts matter in that in-between space, as today's incident shows. For us, the peace of mind was totally worth it.
Edit: The FAA's pamphlet on the topic. Its quite readable, despite coming from a regulatory agency. https://www.faa.gov/documentLibrary/media/Advisory_Circular/...
However, an infant is much safer in a car seat strapped to their own seat of course.