Does removing anti-skating really improve sound?

Better setup is better than better tweeking.  

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 

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.