Airports get a lot of money from parking and access fees. They're not going to willingly give that up, so useful airport-access transit (other than for airport workers) is rare in the US.

Getting on or off BART at SFO incurs an airport fee - though at least it's not a separate fare like the AirBART at Coliseum. The ride all the way to Millbrae is longer but cheaper. The Samtrans buses are normal fare for the zone, but they're hardly what most airport users would look for. And even for other modes: taxis, shuttles, and Uber/Lyft that are licensed to operate (especially, pick up passengers) at any airport have to pay substantial vigorish for the privilege.

But then, airports are mostly (even if city- or county-owned) independent, self-funded operations. Some even pay a profit back to the general fund of the government unit they are related to. It's a rare (and probably failing) airport that needs operating subsidies. Even capital improvements are usually funded by bonds issued by the airport authority, not the local government. So you have to expect that every opportunity to make a buck (or even a dime or a nickel) will be embraced. Transit to the airport either has to pay up or will be limited to a connection that makes sense only for the on-site workers. Ever notice how much more Starbucks costs at the airport?

Anybody who thinks LAX was being deliberately obstructive to transit access by the Green Line, Crenshaw line, or most other local transit is absolutely right. With a peoplemover, the airport can charge an extra fare, and keep it all.