Author notes that there is still a standing offer to answer questions for free "if time allows" but doesn't get any inquiries. I believe this shows that it isn't due to fame or the payment making the author seem more legitimate.
Instead I think that the payment creates the expectation that the inquiry will be answered and when someone expects an answer they are more willing to inquire. When the consultation is free or "time permitting", then it might simply be refused but making the inquiry itself isn't zero cost for the individual and their mental calculus makes it not worth asking. The mental calculus is, "What is the person getting out of this interaction and why would they choose to answer me but not someone else?" When it is financial you can see that you are equal to everyone else and you see exactly what the consultant is getting out of it.
Instead I think that the payment creates the expectation that the inquiry will be answered and when someone expects an answer they are more willing to inquire. When the consultation is free or "time permitting", then it might simply be refused but making the inquiry itself isn't zero cost for the individual and their mental calculus makes it not worth asking. The mental calculus is, "What is the person getting out of this interaction and why would they choose to answer me but not someone else?" When it is financial you can see that you are equal to everyone else and you see exactly what the consultant is getting out of it.