Point a webcam at the screen and wire a mouse to the computer controlling the webcam, you'd have to simulate the computer moving the mouse like a human would but I don't see why it wouldn't work.
I can see it being possible - racks of "robot arms" that move mice based on whatever criteria is needed (in this case, reCaptcha).
It works for 3D printing, as well as device testing - so in theory, this could be done too...
It’s always going to be an arms race I guess.
It exists for a long time already.