Kata is hard for the uninformed to grasp. Kumite is interesting enough, but its fighting, and anyone can learn to fight. But everyone, and I mean everyone, can appreciate tameshiwari. Everyone knows how much their hand hurts when it hits hard objects by accident. So when they see someone transcend normal human limitations, it gets their attention. Regardless of what you or I think of breaking, that is how over 90% (my off the cuff estimate) of non-MA-ists see it.
Everyone finds the idea of transcending mortal limitations appealing. If they didn't kids wouldn't run around with red bath towels converted into capes pretending to be Superman, nobody would buy toy light sabers and pretend to be jedi, and nobody would have bought Chemtoy's Spiderman Webmaker back in the seventies (I saved up my allowance to do so).
We have an inborn desire to transcend our limitations. Tameshiwari allows us to endulge in that fantasy for a brief moment. After we understand it, we then may enjoy the reality that our limitations weren't quite as limiting as we thought they were.