I think pass two is intended to introduce additional regions of concavity (mostly by replacing straight lines), which in effect introduces a bunch of inflection points, helping creating the organic "spiny" feel, as opposed to a "bubbly" feel. Without it, the resulting caves look a bit more like if you spilled liquid on a waxy surface, and less like thorns.

If you go into the javascript and replace "for(let p=0;p<3;p++)" with "for(let p=1;p<3;p++)", and then re-execute the block in the console, you can generate run through a bunch of generations without step 2