Exactly. House T'Rump says "No way are we uniting houses, we're gonna make the empire great again. Starting with the great Tribble hunt."I think they could do this and touch on the political situation in the US. A new Klingon leader who wants to "Make the Klingon's great again". This leader would ban all Smooth-heads from the Klingon Empire which is why we see Smooth-heads in TOS. All the ridge-heads are back home.
After typing this, I feel like this should be a joke, but it's really happening.
Now add houses for Russia, China, extremists, etc. and you got yourself a dangerous, contentious Klingon species.
Star Trek works well when the aliens are like us 21st century humans. The federation represents entry-level utopia. Where we want to be one day.
Regarding the smooth heads, they would probably need to be smarter since they are essentially mutated humans, without their exoskeletal parts, increased strength, and redundant vital organs. Not hard to see how these 2 types of Klingons would not get along.