I do mostly NF, COE and Reclamation campgrounds. For those, I absolutely prefer site specific.
When I do rallies at commercial RV parks, we are usually preassigned a specific group of sites. I really haven't seen much difference between the sites in the parks, so the only reason I could see in a site specific reservation would be to park next to a particular person or to NOT park next to a particular person.
As for making reservations, I much prefer online. As mentioned above, it gives me a printout of my reservation in case of a mixup. It also lets me make the reservation at my convenience and not just when the park office is open.
As a business, I would offer both online and phone reservations. I would at least provide an option to select a grouping of sites if not site specific. Something like "would you prefer loop A, B or C?" or " would you prefer east facing or west facing? ", etc. That lets folks have some input into their site without forcing them to pick blindly. East or west facing is nice because the guest could select based on their window configuration and if they want the morning or evening sun, etc. Just be sure to clarify if "east facing" means the back of the site faces east ot the front of the site.
