Yes, I see the problem. And I can see how attaching a motor to each disk would get around that problem. But you would need a home sensor on every wheel, and you couldn't drive the motors with the same signals, because that would prevent you from getting each to is home position.
To my mind, the biggest problem with using a motor for every disk would be that somehow the cleverness and coolness of the original cog design is gone. For me, what made it so cool and clever was that it did what it did with such a simple mechanism. It seems too simple to make the patterns it does, and yet it does it. That was the surprise. But with a motor on every wheel, of course you can do whatever you like or want. A complex mechanism making complex patterns is to be expected, the surprise is gone.
Do you get what I mean?