Does removing anti-skating really improve sound?

Lewm only in a straight line. If you rub your finger against smooth glass at a specific speed and pressure you will encounter a certain amount of friction. If you rub your finger across 100 grit sandpaper at the same force and speed you will encounter more friction aside from taking your skin off. The groove is not that rough relative to the size of your finger but Newton's third law applies. In order to move the stylus relative to the cartridge and tonearm you have to apply a force which is what the groove does. The equal and opposite reaction is friction and heat. Unfortunately, the situation is so plastic given the variation in frequencies in combination I do not think there is any math to describe this. You are right about the effect of straight line speed on friction but a groove is anything but a straight line. The coefficient is probably not constant given the changing frequencies but I do not know this for a fact and I will try to fine academic support for that theory. I also think I can arrange an experiment. I can set the anti skate via a test record then play a smooth side at the same distance from the spindle as the test track and see which direction the tonearm slides. I'll get back with the results.

ct0517 try it with a test record. Don't break the wires!

Oh Lewm, The speed of the stylus through the groove depends on the groove velocity not the speed of the record. The higher the modulation and frequency the faster the velocity. The stylus is traveling a longer distance in a given period of time

Duh! That's what I mean about changes in velocity, which are "accelerations" that generate a force in the horizontal plane. As the stylus bangs into the vinyl while traversing the modulations, the force due to acceleration ADDs to the "normal force" (Fn in the equation), pushing the stylus against the vinyl, thus momentarily increasing friction and therefore the skating force.  Like I said, we are not really in disagreement; I am trying to use the correct language to describe what I think is happening.  But it's got nothing to do with steady state velocity.  Playing a 33 rpm LP generates no less of a steady state skating force than does playing a 45 rpm LP, even though the steady state velocity is greater in the latter case (groove modulation notwithstanding). 

@ct0517 ,

It seems the quote from the VPI manual makes my point. A complete turn either way gives way too much counterforce to be useful.

I should have mentioned I use the string/weight anti-skate VPI provides.