Just throwing in some series logic here. It's silly to say one can "claim" the Mazo and play keep-away from everyone else, and silly to say that once it's on the Tailed Beast list, it can only be challenged for.
Stay with me here, but let's see what happened in the series.
- The Gedo Mazo is the dried-up husk of the Ten-Tails, sealed by Hagoromo in the moon and guarded by the Hamura and the Otsutsuki Clan. This is what it was originally intended to forever be.
- Then Madara comes along with his newly awakened Rinnegan in his old age and summons it straight from the moon and in his lair.
- Nagato is later shown to summon it wherever needed, because he has Madara's Rinnegan.
- Obito pulled the same trick too, and only needed one Rinnegan to do it.
- Then after Madara got one of his Rinnegan back after being revived, he summoned it straight out of Obito where it was still sealed within.
See the picture here? It's become a moot point to claim and/or seal it if
anybody with at least one Rinnegan can summon it out of the blue. It doesn't matter if you're the Sage of Six Paths himself and sealed it within the moon, or just a mook who hid it in a cave. It's really easily usable if you have a Rinnegan. Sure you can play tug-of-war with it, but then nobody would really be able to use it. A better idea would be just to stick explosive tags or Hiraishin markers on it.
If anything, here's a compromise I would like to propose:
Add it to the Tailed Beast list, and then create a rule where it cannot be summoned and/or used other than by the holder of it.