I've experienced quite a few humans who, when driving an automatic, seem to select a speed and throttle position that keeps the transmission right at the top of a gear range, with the engine turning much faster than necessary, instead of going slightly faster and letting it upshift. I doubt that's fuel efficient at all.
Even with an automatic the driver has influence on which gear is used, and a driver who naturally doesn't need to know about gearing may unintentionally be telling the transmission, via other inputs such as throttle position and speed, to select too low a gear than what a manual driver would choose.
(For instance, one of my cars has a manual gearbox with an electrohydraulic actuator system and an automatic clutch, operated by flappy paddles. My insurance company says that it is an automatic, while the equivalent of the DMV (correctly) states that it is a manual.)
I drive a manual and I know exactly why it is not fuel efficient: the idiot behind the wheel :-)
My own anecdote is that I'm a better driver in a manual. I'm a lazy driver, and lazy in a manual means avoiding stopping/gear changes by anticipating green lights and so on. Being lazy in an automatic results in more stop and go for me because it's no more effort. I could be as efficient in an automatic, if I put in the effort (which I would probably do if I knew my numbers were going into a study).
Other modern cars have an "eco display" or similar, which gamifies the experience. My previous car had some progress bars for different aspects, and I spent several boring commutes trying to get to a perfect 100%. (I did it once, I was so happy! Usually only got it to 98% before I hit the city and got stuck in traffic again)
Making automatics more efficient is a technological optimization problem. Making manuals more efficient is a human skill problem. I know which side I'd bet on in the long run. (Hint: Not the human)
That has the potential to be really dangerous though, at least where I drive(a third world country). If a car doesn't do what you expect it to when you provide a certain input, that's a recipe for disaster.
Large six cylinder revving to mid-range (say, 7500) with ample torque at all range can drive the car in overdrive even at city speeds, but an automatic will treat most change in throttle as a downshift. Because they have no ability to understand your intent.
I guess self driving car with an automatic can really fix that, especially because they can get geared optimally to the driving inputs the software tells them and they have 'inside brain' information.
I'm not sure I buy this. I noticed when I switched to automatic from manual I would drive in ways I would never have done with the manual because, well, it was easier than having to care about RPM, target speed, and current gear state: I'm not worried about automatic drivers being bad drivers, I'm worried about them not caring.
Here's the site: http://www.autoweek.nl/verbruiksmonitor
In a measured test, with a skilled driver, who does the right thing for the entirety of the test, it is most likely that he or she will be more efficient with a manual transmission than with an automatic.
However, in real life, for real humans, over a longer period of time, the drivers with modern automatic transmissions will be more fuel efficient than drivers with similar cars and manual transmissions, because the automatic transmission is a reliable machine that will do the same thing, every time. It doesn't care if you had your morning coffee or not, if some asshole cut you off, or if you got distracted or bored or spaced out and forgot to change your gear to the right one.
And, disregarding the disruption the EVs will be, technology constantly improves, while human skill is fairly constant, so it was just inevitable that automatic transmissions would one day overtake manual transmissions in terms of speed and efficiency. Arguing otherwise is just irrational nostalgia.