I assume most wet labs have robots that do part of the workflow. But they are mostly useful for automating repetitive tasks, and need a lot of setup before they can get to work.
For small experiments, when setup is 90% of doing the job, then you just don't win much by letting a robot do the remaining 10%.
The university lab I interned in had a 96 well pipetting robot that was shared between a few research groups. I never used it. I think it was mostly useful if you wanted to do an experiment many times with varying parameters. But for most of the stuff we did, the steps were just not repetitive enough that programming a robot would make sense.
Also, there are usually a lot of steps between the pipetting that the pipetting robot couldn't do like loading stuff in a centrifuge, checking DNA concentration, putting it in the PCR machine, etc.
Not your typical liquid handlers sure - but advances in robotics like Robocat type things should mean you could build a much more general robot that could operate much more like a human in a chain of tasks.
Programming the robot, and putting the and register the reagents and source material.
Given that they can produce instructions for humans, I don't see why they could produce instructions of the robot ( with perhaps some human instructions for making the reagents and source material etc available ).
A lot of traditional liquid handling robots are large and have relatively large buffer tanks etc - so need flushing etc etc. But I don't see why you could use something like RoboCat to be much more flexible for simple container to container pipetting.
For small experiments, when setup is 90% of doing the job, then you just don't win much by letting a robot do the remaining 10%.