Omsed,
No one is talking about spinning a complete turntable, or that there is a centripetal force involved in the skating issue, or that the cartridge is spinning with the record. If you read all the posts here and elsewhere I think that is clear. The only reason for using the term at all is in attempting to try and clarify the difference between a force acting toward the centre in the context of an arm being spun or a body in orbit, and a force acting towards the centre in a tonearm in reaction to the friction in the groove.
VTF is, of course, different on each groove face unless anti-skate is used. That's why the skating force is a problem. That is elementary. I don't get what you are saying re the groove faces being identical etc. We are not talking about record cutting, but playback.
Regarding information storage, if I store the same information in a bigger space, that's all I have done. When I retrieve it, I get it back. The point about the bigger space is that I can store more information, otherwise what's the point? Perhaps I am wrong, not being a recording engineer, but I was under the impression that higher speed allowed higher levels, whether it be tape or vinyl. And if there is more information, of whatever kind, the cartridge has to do more work to retrieve it, hence the reference, albeit imprecise, to energy (I take your point about the irrelevance of the platter's kinetic energy).
As you are having difficulty finding proper scientific papers, I've posted a link
here. Look at Gilson and Alexandrovitch.
John
.