Does removing anti-skating really improve sound?

Lewn Theoretically you are correct in that varying tangency will change the force vector but in real life the error is so small it does not account for much. 
You are mistaking velocity with record speed. As the modulation increases so does velocity. In a heavily modulated groove the record has to exert more force on the stylus to move it and the stylus is moving faster. In a straight groove the record is applying only straight ahead friction and the stylus is not moving (through space) at all. The energy (work) required to move the stylus is seen as friction and a little heat. You could make the argument that anti skate does not decrease towards the center of the record because actual velocity does not change. There are just as many squiggles they are just closer together. And indeed it does not change as much as you would expect given the vast difference in groove speed between the outside and inside of the record. I did make a miss statement earlier when I said velocity decreased towards the inside of the record. It does not. Groove speed decreases towards the inside of the record. What would be nice is a test record with a bias band an entire side. That would be fun!

I haven’t read through this thread but here’s my take...

On my VPI, (we know Harry doesn’t advocate anti-skate) I haven’t noticed any difference in sound with or without. It just makes perfect sense to use it for the health of my records. As long as your azimuth is good, that’s much more important for SQ.

On my VPI, (we know Harry doesn’t advocate anti-skate)

From the VPI owners manual

As mentioned earlier, the arm wire applies the anti-skating force. The degree of force applied can be adjusted, to increase anti-skating force give the connector a counterclockwise twist, unwinding the wires natural twist. Likewise, to decrease the force, give the connector a clockwise twist, winding the wires natural twist. Remember, the Lemo connector can only be "adjusted" in increments of whole turns. If it is not, its key will not line up with the groove in the receptacle 

Removing antiskating does not improve sound, applying too much ruins it. All depends on stylus shape and cartridge suspension.

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.