At best, any compensation is just a rough average of the force that is required to compensate for skating forces, the actual skating force varies greatly due to different operating conditions. In particular, there is more skating force when the stylus is tracking highly modulated grooves (loud passages). Some people set anti-skating by playing test records with higher and higher levels of play and then use anti-skating to compensate for distortion appearing in one channel (if the right becomes distorted, increase anti-skating). The problem with this approach is that it applies too much compensation for more typical playing conditions.
Even though playing a blank groove does not reproduce actual playing conditions, it is used as a rough proxy for methods where you set anti-skating to cause a very slow drift toward the spindle when playing a record near the end of the record. This method has been endorsed by a number of stylus/cartridge manufacturers who know a thing or two about wear on the stylus. I like this method because it is easy. You don't even need a blank record. Put the needle down in the run-out section of a playing record and watch which way it drifts before it catches the groove. You can look up Peter Lederman's (Sound Smith) videos on the subject.
As to the persistent issue of what causes the skating force, it is caused by friction of the stylus playing the groove. The direction of that force pulling on the cantilever is roughly 90 degrees from the line between the two sides of the stylus contacting the groove. For the most part, that means that the force is pulling along the same direction as the cantilever itself. If the arm were straight, with no offset angle, the pull will be against the arm pivot. But, when the cartridge is set at an offset angle, the direction of pull is no longer toward the pivot. I have a simple way to demonstrate this phenomenon. Place your elbow on a table and hold your arm straight out and then pull your middle finger straight back. Your arm will not move because there is no sideways force. Now cock your wrist toward the right, like the offset angle of a tonearm. If you pull straight back on the middle finger like before, your arm will swing to the right. This is precisely what happens with your tonearm.
S-shaped arms are no different from other arms when it comes to skating force because the cantilever on the cartridge is not pointing at the pivot. That shape was chosen to balance the weight of the arm at the pivot.
Even though playing a blank groove does not reproduce actual playing conditions, it is used as a rough proxy for methods where you set anti-skating to cause a very slow drift toward the spindle when playing a record near the end of the record. This method has been endorsed by a number of stylus/cartridge manufacturers who know a thing or two about wear on the stylus. I like this method because it is easy. You don't even need a blank record. Put the needle down in the run-out section of a playing record and watch which way it drifts before it catches the groove. You can look up Peter Lederman's (Sound Smith) videos on the subject.
As to the persistent issue of what causes the skating force, it is caused by friction of the stylus playing the groove. The direction of that force pulling on the cantilever is roughly 90 degrees from the line between the two sides of the stylus contacting the groove. For the most part, that means that the force is pulling along the same direction as the cantilever itself. If the arm were straight, with no offset angle, the pull will be against the arm pivot. But, when the cartridge is set at an offset angle, the direction of pull is no longer toward the pivot. I have a simple way to demonstrate this phenomenon. Place your elbow on a table and hold your arm straight out and then pull your middle finger straight back. Your arm will not move because there is no sideways force. Now cock your wrist toward the right, like the offset angle of a tonearm. If you pull straight back on the middle finger like before, your arm will swing to the right. This is precisely what happens with your tonearm.
S-shaped arms are no different from other arms when it comes to skating force because the cantilever on the cartridge is not pointing at the pivot. That shape was chosen to balance the weight of the arm at the pivot.