There's no obvious reason why airports charging people who use the airport as a transportation hub is unreasonable or onerous by definition.
Therefore, any charge that moves from services provided, on a needs basis, to an indiscriminate tax, on a per person basis, can be seen as onerous in light of the public investment.
If they meet the car at Walmart do we expect the walton family to get a cut? If they drop the car off at their home do we expect the HOA to get a cut?
At some point we could acknowledge that the airport isn't a party to the transaction.
Starbucks has decided that a fairly open access policy for non-customers conducting other business is a net positive for their business. Many businesses have different policies because they have different actual or perceived business dynamics. Also note that most Starbucks do place limits on this, as people who mistake them for zero-cost unlimited co-working space tend to discover.
> Which turns into a tax
A tax turns into a tax? Tell me more about this theory...
The first is congestion due to the pick-up process. Clearly, this affects both the new players and the old players. The second reason is land-use by the parking lots in which available cars are stored. This doesn't affect the new players. Now, airports might be charging for both, and simply be afraid that the cash-cow of charging reasonably for the land-use of parking lots is going to disappear.
For a real answer, you'd need to actually compare the difference in cost between congestion and land-use.
Having a driver meet you with a car at the terminal is a much better experience IMO, whether it's a taxi, a Lyft, or a rental. If the pickup area is too congested, the airport should address that problem directly with a toll to access that area. A targeted ban that happens to help incumbents in a particular industry doesn't seem like the best way.