It is impossible to roll a 1. A 2-sided die will always land on 2.
Not only that, but since a new die will never have more sides then the one you used to roll, it will always generate another 2-sided die.
You're right. I decided to not let the game roll ones since it would slow down the score progression to a halt, but I may reconsider that strategy or at least mention it in the rules. Thanks for playing!