So you leave the goat head in? And this process works?

The one downside I see is that if the goathead sticks in the tire and your put the tube back in and the prikker on the goathead pops a new hole.

Back in the day in the shop, we'd remove the tire, invert it, feel carefully for any remaining sharp edges, remove them, and then fix or replace the tube.

Bu to your point, one flat fixing kit for tubeless tires suggests that you superglue any cut on the tire exterior and then patch the inside of the tire.