One theory is that as autonomous cars and ride sharing services become popular, they end up as gateways to public transit--especially rail/longer haul mass transit.
I disagree.
Fundamentally long haul mass transit is a tiny amount of passenger miles traveled. Right now it's a drive/bus/rail/air conundrum. Reduction of personal auto ownership will certainly increase the bus/rail/air component of long-haul travel, but it'll still be a tiny subset of total vehicle miles traveled.
See here:
https://www.bts.gov/content/us-vehicle-milesLong haul via transit today is <1% of total vehicle miles. I can't break out what percentage long-haul car transit exists, but if it's higher than 5% I'd be shocked. So even if it results in a HUGE increase to rail/long haul transit, that's not that big of a difference to total vehicle miles.
Short-distance transit will forever have its own problem, however. When you have to take 50-60 passengers (bus) or a few hundred passengers (light rail) from point A to point B, you need routes that are common to those passengers. Every 1000 feet of deviation from the pickup or dropoff points hurts your adoption of transit because that's distance that must be walked. What good is transit if it drops you off 1.2 miles from where you're going?
What autonomous cars and ride-hailing does is move us to a more transit-blind mindset, where people perhaps take buses or rail when it happens to be going where they want or use ride-hailing services when transit doesn't go where they want. I suspect that transit should end up cheaper per-mile than ride-hailing, because of network effects, so it would be a reason to use transit if it happens to go where you're headed.
Still, for too many people, the idea will be ride-hailing from home to a transit station, riding transit, then ride-hailing to the actual destination, and I think that in a GREAT many cases that will be both more costly and more time-consuming than just ride-hailing from home to destination.