There is viable public transit from SFO to the city. Both Caltrain and Bart have decent connections to the airport.

Practically, travelers with heavy check-in bags prefer taxis. Public transit can't be the answer for everything.

Without heavy check-in, transit is a great choice. Alas, some problems remain. Many residents consider BART unsafe. Frequency is pathetic for a major subway line. BART is unusually expensive ($14! - 6$ + 6$ + 2$??) and last mile connectivity is bad.

On the topic of cost, other airports that are on the transit corridor (LaGuardia NYC, Boston Logan, Ronald Reagan Washington) cost $3-4 for the trip. EWR & JFK are more expensive, but they're often faster than taking a taxi which allows them to compete on pricing.