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".
There's another purpose, politicians must be able to stand up (on the TV, press releases etc.) and say they are doing something. Other people/newspapers/tv shows will ask "Why aren't you doing anything about $TOPIC?" ($TOPIC in this case is 'terrorists', and '$NAME doesn't care about terrorists' is not soemthing politicos want to see)