Brad, back in the Old Daze, before slipper clutches, the dragsters (and other classes, no funny cars then) smoked the tires most of the way down. Smoking the tires was the show & fan loved it. When the cars started running slipper clutches, fans hated it cuz no smoke from the tires, altho they did small burns outs to heat the tires. When the funny cars came in, they eventually did long burn outs, cuz they had a transmission & could back up (dragsters didn't then). Fans liked the burnouts & it became part of the show. Funny cars had no side windows & smoke would billow out that part of the body. It was cool to see! The Chi Town Hustler was the king of the burnouts and I think it was their burnouts that got the rest of the floppers doing it was well.
If you can find some old videos of funny cars doing burnouts you'll see what I mean. Funny cars became more popular than dragsters cuz of burnouts & dry hops. that became "The Show". That has all changed over time to where it is now, but older drag fans remember that stuff & how exciting it was to watch. Think of a funny car doing a long, smokey burnout. The back to behind the line, pour some more VHT traction compound down, another burn out, back up, do 3-4 dry hops to the starting line. Really builds up excitement for the run, so much that the run is almost anticlimatic.
So this is the Official Cliff Morgan explanation, FWIW. $2 please.