Stuff like gyro ball are listed as having blank base powers, so why can't they do the same for z-moves?
Generic Z-Moves get their Base Power from the base move. A Base Power of 1 was most likely set to ensure it does not cause weird behavior in case the move were hacked into a moveset, from which they don't have a base move. (Though I'm now curious if a crystal-free Z-Move can be used as a base move for a Z-Move. Say, Shattering Psyche based off Genesis Supernova)
Signature Z-Moves don't have that issue as they only have one base move - hence, the Base Power is fixed because it does not really cause any difference.