With that said, I was still able to start a fire with the broken ones, it was just a bit harder.
Absolutely. I have ferro rods that I have broken deliberately. One is designed to fit in a small PSK tin. Another I carry in a money belt. They are about an inch long; that's enough to make sparks and start a fire, at least under reasonable conditions. I appreciate that with cold hands it won't be as easy, but these are backups stored in places that a full-sized rod would not fit.