I also wouldn’t want a corporation deciding what risk I should take. That’s why I support safety ratings. They’re probably not practical for airplanes, but they work well for automobiles. The government tests how safe cars are and then lets me make an informed choice between buying the safest car or prioritizing something else.
As for greed: price discrimination is the reason why airlines have all those charges for things that don’t cost anything to provide. It actually benefits people who can’t or won’t pay much at the expense of people who can and will. (Of course it benefits the airlines too.) Here I trust greed more than I trust government regulation because deregulation made tickets a lot cheaper. Even the Atlantic (not exactly a conservative publication) is in favor of fees because they make flying more affordable.