Why are all these robots staring at me?

Ah, the Massive Eye. Such a comforting symbol, and not all reminiscent of omnipresent surveillance or literal towers of evil from Lord of the Rings. Which must be why so many tech companies have chosen to adopt a huge eyeball as a central design aspect of their home robots.
Just this week, we've seen appearances from two new eyeball-focused bots: the Big-I (which looks like a felt trashcan with a bowling ball stuck on top), and Moorebot (a smaller device that boasts an "eyeball da