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Q: Why do (some) puppets don't get cores?
A: Reichskommissariats and Japanese General-Gouvernments will not get any cores, because for balancing reasons and because the territory is realistically occupied. So there it is intentional, not a "major bug".

Q: Is there any way those puppets can combat resistance themselves?
A: Their manpower and equipment should mainly go into combating resistance. An exception would be the Japanese puppets, as far as I am aware, they are more restricted by the vanilla functions compared to conventional puppets, or even the Reichskommissariats, which could mean less strenght while trying to combat civil unrest.