It's a good question - and we can gain some insight by looking at cities with much better rail service to their airports.
The baseline is the JFK AirTrain, which carries 11,000 riders per day, out of an estimated total of 5.6M daily subway riders (not counting commuter rail), against a total flyer volume of ~60M a year.
The Heathrow Express, which does take you straight to the terminal, for example carries about 17,000 riders per day, out of an estimated 7M total daily Tube riders (not counting commuter rail), against a total flyer volume of ~78M a year.
Another data point: the BART SFO station (also direct-to-terminal) carries about 6,500 riders per day, out of an estimated total 423,000 daily riders system-wide, against a total flyer volume of ~50M a year.
It's not all doom and gloom - we also know that Narita Airport was able to double its proportion of passengers arriving/departing by rail by improving service. But even if the same results can be replicated in the US - the baseline numbers are so low that the increased ridership would still represent one of the smallest parts of the overall transit system.
FWIW I'm one of the beneficiaries of these rail links, and I'm very grateful they exist - but these projects are ultimately more about signaling/politics/PR than they are about shrewd allocation of infrastructure spending.
About the Heathrow Express. Its ridership is low because the Piccadilly Line (1 of London's busiest lines) also terminates at Heathrow Airport. Most people I know take the Piccadilly Line instead of the Heathrow Express to the airport to save money.
Yeah, Heathrow Express makes sense if you're ending up near Paddington but otherwise I don't really understand it. If there are a couple of you with luggage, get a car and it's door-to-door. Otherwise take the tube and save a bunch of money. I go to London a lot and mostly take the Piccadilly Line or sometimes a cab at off-hours or from inconvenient locations. But I honestly don't understand why the Heathrow Express would be interesting outside of a narrow range of circumstances.
BART SFO is technically direct to terminal but only because you change to a specific spur line. This is similar to the JFK air train and seems designed to support the taxi union. Each such change cuts the number of poss Le riders dramatically, especially when lugging bags.
I take BART to and from SFO all the time. But then I'm essentially always just with carry-on. Pretty much any public transit from airports (with the possible exception of busses explicitly set up for the purpose) aren't a great fit for travelers lugging a bunch of suitcases.
