Neither Kid and Law have direct fleets or allies. This is why they will not be PK competitors. Unlike any other Yonko (past and present), they do not have allies to help them deal with other Yonko's overwhelming presences.
Luffy would have died at WCI if he could not escape. Wano would have been lost if they didnt have a 5000 member army and a huge alliance.
Kid cannot defeat Shanks, 8 other commanders, Giant allies and whatever other captains comprise Shanks' fleet. Neither could Law. This is why the SHF exists, to deal with stuff like this logically.