Earlier quoted context omitted.
No, the TSA exists because 19 people hijacked 4 flights and succeeded in crashing 3 of them into various important buildings in the US on 9/11/2001. Private planes are just as capable of crashing into buildings as commercial jets. The TSA has picked up some ancillary public safety functions over the years, but their raison d'etre is to prevent hijackings.
In terms of menace potential, any private plane will lose to a van full of fertilizer and a baddie intent on causing destruction. It's a matter of scale. Little planes, like this one [1] just don't do damage on the same scale as airliners. [1] https://en.wikipedia.org/wiki/2010_Austin_suicide_attack
(But regardless, it’s not clear that the TSA is even performing that kind of calculus.)