Does removing anti-skating really improve sound?

With my 12" Jelco and two 12" Groove Master tonearms used with Denon 103R, Audio-Technica Art9, Audio-Technica 33Sa, Benz Ace, and Soundsmith Zephyr cartridges little or no anti-skating sounds the best.  My two 12" Schick tonearms have no anti-skating.

When I used a 9" Jelco I again found very little to no anti-skating sounded the best. 

My opinion is what sounds the best is the best for my cartridges.

It’s difficult to reason that not setting the anti-skating will produce better sound reproduction. Reducing side loading on the  stylus cantilever should result in minimal side loading and damping of the mechanical function of the system, hence allowing for maximum possible accurate reproduction and channel balance, but I don’t discount  empirical data either . 

My two 12" Schick tonearms have no anti-skating.

I've owned one, nice looking, but relatively cheap tonearm from a DIYer, designed for SPU and Denon 103 (both with conical tip). All new versions of the Schick toneams now have anti-skating! 

If you want to save your records and stylus tip you have to use anti-skating. 

Actually Schick arm is the only one without anti-skating out of at least 10 very nice tonearms (vintage and new) i have tried. 

I think that statement that the sound is "better" without anti-skating is an urban legend. 
 

lewm

... The skating force is generated by the friction of the stylus in the groove ...

This is mistaken. While stylus shape can influence skating force, the actual cause of the force is the pickup arm offset. That's why true linear tracking arms have no skating force. There are also a few pivoted arms that have no offset; they also have no skating force.

Cleeds, with no friction of the stylus in the groove, there is no skating force. Head shell offset angle is one cause of lack of tangency to the groove that from a vector force point of view gives rise to the force that pulls the stylus tip toward the spindle. However without friction headshell offset wouldn’t make one single bit of difference, and there would be no skating force. That is the genesis of my remark. And by the way, headshell offset angle is not the only cause of the skating force as far as the geometry goes. Skating force is further augmented by lack of tangency to the groove wall at any point on the LP surface that is not on the two null points of a typical alignment algorithm. Only at those two null points is headshell offset angle the only cause of the skating force. Everywhere else on the LP surface the two geometrical errors that result in lack of tangency are combined.

In addition, you are so so wrong about tone arms that have no head shell offset angle.

 There is a lot of wrong information and subjective opinion in the above comments. I hope the OP can sort it out. I would advise the OP to talk to a person that knows this subject, or to do some Internet research looking for the comments of knowledgeable people.