Does removing anti-skating really improve sound?

it depends on the stylus tip profile, it's better to use antiskating if you don't want to destroy one side of the vinyl groove wall 

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. 
 

No AS results in a more open sound. By contrast, AS brings greater focus and more stable L to R image. It also enhances the bass somewhat.

brilliant ears, lol

The thread in your arm will also dampen its movement and resonances. Over the years I have run my tonearms (VPI, Sumiko The Arm, Grace 840FB, Lustre GST 801) without AS, without harm to my styli or records.

How can you inspect your stylus, do you have powerful microscope? The professional retippers opinion is opposite to yours. I also have Lustre GST-801 and the sound is just fine with its magnetic anti-skating.

does an S tonearm require less or no antiskating? Is it an inherently better design?

No. The anti-skating must be equal to the tracking force. It can be slightly lower than tracking force if your stylus profile is something like MicroRidge and related (i remember this from Van den Hul interview). 

Why don't you just stick to conventional golden rule instead of some exotic methods? 

Buy yourself this TEST LP there are special grooves calles "Bias Settings" to set-up anti-skating correctly on any tonearm with any cartridge/stylus. You will actually hear why do you need anti-skating.  

@lewm

Chakster, probably you shouldn’t disseminate the idea that VTF should equal AS. .... But read Doug Deacon’s old thread on AS with Triplanar tonearm.

This is not my full post, as i said there is a special Test Record to set up anti-skating correctly by actually hearing what the anti-skating can do with the signal coming from that test record. I also said that Van den Hul recommended to use lower anti-skating for the most advanced stylus profiles.

I can add that some High-Compliance cartridges with very low tracking force (1.25g) can jump all over record surface without anti-skating.

A Tri-Panar tonearm has fluid-damper full of silicone, many conventinal tonearms does not have this feature and result is different.

A well known retipper also claimed that he can see the effect of incorrect anti-skating on one side of the diamond under micro scope. 

You can prove this to yourself with any good test record like the Hi-Fi News Analogue Test LP. Play the Bias Setting band and lift your anti skate weight. The left channel will start buzzing madly. Add a lot more weight and the right channel will start buzzing madly. Get it right and both channels play the test tones beautifully. This is the only right way to set anti skate and it is at best an approximation as the skating force changes with groove speed and degree of modulation. Any setup that sounds better without anti skating was not set up correctly to begin with.

I'm glad someone else has mentioned Hi-Fi Test LP finally. 
Because people normally posted something like "adjust by ear or using CD or blank record" 

Hi-Fi Test LP is a must have, not only for anti-skating, but for eoverall setup, there is a free protractor inside. 

@mosler666 you can't judge about your stylus condition with pictures like you have posted. 

If you want to see how close you have to get to the stylus with a nice microscope read this article.