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.
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.