So if you're suggesting the airport be privatized, and then offering services like any other "business entity… deciding what to do with its own property", I think that'd be a great plan.
But SFO is a public entity, using state power to enforce extra monopoly privileges. It doesn't get to just say "because we want to do it this way with 'our' property", even if it's silly. It's the city of San Francisco's property, and their actions should be serving the public interest.
An equitable regime of charging based on actual visit impact achieves that. On the other hand, enforcing the old formulas out of tradition is lazy and destructive - and suspiciously protective of SFO's longtime partners among the incumbent rental agencies.
We still have state owned toll roads across the country. There is an established habit of limiting road traffic via tolling even on public roads.
Toll roads (state owned or private) charge by use, which is fairly reasonable and efficient, not by a deep inspection of your gross revenues.
The visit toll could be collected electronically, via transponder or a bill mailed to the car's registered owner, to require no slowing or stopping of traffic.
They could also allow free or cheaper visits at the far end of the SFO 'airtram' (where the existing rental car center is located).... the differential could even vary with congestion.
If they want to throw a bone to occasional, casual flyers and friends on pickup/dropoff duty, let each license plate have 1 free visit each N days. (Though, the logic and fairness of charging every visit equally based on its congestion impact is strong.)
There are better ways to meet any legitimate concerns of SFO than to force new services into the old rental-agency cookie-mold.