Ahriman
Tyrant
If you blocked puppets from earning culture, you would also block them from building culture buildings.It's an interesting idea, but that would make the situation worse I believe. Right now people are ripping their hair out when a puppet builds a barracks. That's only a 1 in 4 chance of happening most of the time. Imagine how frustrating it will be when puppets start building temples that don't give benefits?
Also, not sure where you get 1 in 4 chance from, every puppet builds a barracks as ~its 3rd-4th building (nearly always monument, temple, barracks), and an armory at ~6th building.