If we take the same $ and get rid of the drivers we can run twice as many buses and that increased service will get a lot of riders who previously thought the service was too bad. Though you will need to run the additional service for a few years before people figure out service is no longer bad and start using it.
Now we do have to assume some intelligence in bus routing. There are a lot of bad bus routes in cities that will never get more riders because of how stupid they are.
Of course you are right that politics gets in the picture. Rail gets far too much attention for projects where the lowly bus is cheaper for otherwise identical service (and where rail is needed it is often done wrong). As already pointed out unions will hate this plan and they have power to screw the rest of the population (who because they don't ride now don't think they would if this plan happened) and the environment (they care about the environment only after their own self interests.
Still the numbers work on paper: self driving buses should get a lot more riders on yoru bus system because you can afford to run more service.
On rail I'm not as sure but on bus yes. Drivers are the largest cost associated with a bus line. There's also a whole set of downstream costs like bathroom breaks which requires that routes are aligned with bathroom stops and that bathrooms are kept in good working order. Breaks also decrease bus frequency (humans need breaks!) and running more buses is often limited by the number of drivers you can hire.
However bus drivers often play a dual role in US transit of discouraging anti-social behavior so it's unclear to me if you could even get rid of the bus driver and the associated inefficiencies or you'd just need to replace them with a police officer and deal with the exact same problems.
Many bus drivers are unhappy having to play this role, so that's also a factor.
In the cities I've lived, it's not quite that.
Building rail is a lot of dollars, but politicians are often happy to throw money at that problem. It's good for a dozen industries, like construction.
But that money cannot then be used to operate the rail long-term. That burden is on the city entirely.
I've lived in two cities that turned down millions of dollars in federal transit grants because they didn't have the money for maintenance and operation.
Putting maintenance into that capital bucket though is accounting fraud and illegal. If you have a rail line the largest cost is regular maintenance which is based on time not wear until you have a very large number of trains running. So my point stands even if you separate the buckets.
https://www.trains.com/pro/passenger/pennsylvania-governor-a...
Someone should let the governor of Pennsylvania know he's committing "accounting fraud."
If buses ran more often, they hopefully would become attractive to a lot more people. Anecdotally, I think most issues happen later at night where there are a handful of people on the bus. Having more people all the time would hopefully discourage anti-social behavior even if it wouldn't prevent incidents.
In terms of bathroom breaks, I've seen the driver pull over to use the mcdonalds or grocery store bathrooms so that is probably "free." There are only a few places in LA metro system where there is a purpose built layover facility where one might imagine there being a metro maintained bathroom facility. Most layover facilities are just dedicated street parking for busses to queue, such as the one at the end of Western blvd and franklin where I've seen the drivers utilize the Lazy Acres grocery store facilities.
It's usually that $transit_company needs $xxx,xxx,xxx to do a good job.
Politicians will only give it $yy,yyy,yyy to do the job.