Done.
Yes, I've seen your two existing robots "in action". A classical piece design will however present new challenges for creating a robot arm that can precisely pick up and move the very diverse pieces in a chess set.
Most pieces have a round top that should be easy to grab. Knights are an exception and could pose a challenge.
OTOH, all pieces have a round base, so the robot could pick them by the base, rather than by the top, as a human would. This should be as easy to do as if they were simple disks.
The speed of the existing models is certainly adequate to their respective purposes. Wether a similar speed can be maintained for a regular chess mechanism remains to be seen.
However, it will never be fast enough for blitz, which is a preferred mode of playing especially in online communities (as well as among young people with their sub-goldfish attention spans). No mechanical machines can ever be fast enough for blitz, it's just not doable.
Of course, many will prefer to play such a computer in a more relaxed atmosphere at home, with longer times per game(move) - myself being one of them. So, mechanical reliability and ease/elegance of movement of the robotic mechanism would be more important than speed. The old Novag Robot certainly moved its arm quite elegantly - as long as it was in working condition.