Does removing anti-skating really improve sound?

Mijo,
check it out:
F = Fn*mu, where F is the force needed to counter friction between two bodies in motion with respect to each other.
Fn is the normal force ( meaning VTF in this argument).
mu is the coefficient of friction.

Where do you see velocity?
Speed is a scalar quantity; this is about vectors. 
Your argument isn’t terribly wrong, except you are resistant to seeing my point that velocity has nothing to do with it; it’s changes in velocity that are causing additional forces. Any change in velocity is an acceleration.

When I used to be in closer proximity to buddies systems, we used to frequent each other. All of the systems , including mine with various pivot tonearms, (still own a Dyna) allowed you to hear, if you listened closely, to the two spots on the record where the stylus was lined up best with the groove, depending on the geometry you are using. Where the stars align for the pivot arm . 

For those few seconds over each spot the focus is definitely - clearer.

IMO - If your anti skate is set up - ok - you should be able to make out these two spots...I mean should you decide to listen in this technical way.

Now an interesting thing... 
 
One turntable where this was definitely not the case, was with a Technics sl1200, with grado black, that I used to loan out.
  
But still .....it sounded good;  which leads me to come to the conclusion that even if off a little, vinyl distortions with a pivot setup are "pleasing in nature" for the lack of a better word,  the technics sl1200 pivot arm still sounded decent.

It's not until you hear better, that you realize the setup is off, from the better pivot tonearm setup.

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