Used to use it in the early 90's, when it was legal, made a big difference on brand new hard tyres, it was a balance to make the tyres last 4 races in a day (try not to get to the canvas by the final). Those days are long gone.
We do this in RC racing and just cover this inside half of the front tyres normally . At least to start with. Cover the whole of the rear tyres Also if everyone was using it it would lay down on the track as well and create even more grip as the day goes on. Tyres will ware quicker as well.
Back in the 90s here in Australia; wets weren't legal, however tyre treatment was legal - so if it rauned, we had to run slicks in the rain. On softened slicks in the wet, the tyres would squeal around the corners, they had that much grip!
you can get kart tyre specific softener that guarantees faster lap times, and i think it goes in the inside usually 🤔so it goes unnoticed and then seeps out when driven, just remove the schrader valve from the tyre stem attach a hose-fill some in, pump back up spin it round and off you go. Well that's what i have heard 😅 You should try it again so we can see the results and what works best (just for the purpose of science ofcourse)!!
the graining effect probably comes from the chemical being used to soften the compound breaking the chemical bonds of the rubber. So, it is overheating the broken surface layer before the core of the carcass is getting hot. thus it is graining up and shedding. i suspect that softener would drastically reduce tyre life.
Also, if the rears are a slightly different compound it may require more coats to get it to work
0:56 the big difference comes on fresh tyres and more so on wets, it’s just to remove the release agent from the top layers so your tyres are optimal for the first few laps before anyone else scrubs off the grease layers