Opens you up to a lot of attacks, and sets a bad precedent for how to manage keys.
Discussion
Which attacks would you be vulnerable to? The code is open source for the stamper so you can review that before flashing. There's no memory to store anything. It has no networking to transmit out. I don't see the attack surface.
Because the more you pass seed information the more inherent the attacks. You should handle your seed as few times as possible.
I don't want stepper motors plotting out my seed. That's incredibly dumb.
Whether or not the device comes with memory installed doesn't matter.
There are very creative people out there.