I think there are two purposes to the TSA. One is to make people feel safe, as you mentioned. The other is to get people into the habit of having their rights routinely violated by "government agents". It is a form of conditioning, and its pretty effective.

10 year olds at this point have never known a world that was otherwise.

In another 15 years, almost all adults will be completely used to it, and the idea that we don't need the TSA will sound as absurd to them, as to most of us it seems "absurd" that in fact in the past you could fly in the USA while carrying a rifle or shotgun aboard, with ammo. The flight attendants would offer to stow it for you in a coat locker, but otherwise wouldn't bat an eye.

Even today you can fly with firearms (in checked baggage) but a lot of people think that this idea is completely absurd because they've never seen it... and they've been conditioned to being disarmed and the idea that you can't have a gun in an airport. (you walk in and check it at the counter, before going thru security.)