Ahriman
Tyrant
So let's take example to the logical end in Civ5. Your Milistanian Civ invaded America, and puppeted NY, Boston and Philly. Then they took Chicago and started to raze it. Their happiness plummeted too low, fairly enough it "costs" more happiness to raze. So what does the Milistania do? Quickly they set aside funds to construct theaters and stadiums all around their offshore homeland. And lo and behold, the entertainment so provided put the conquered American citizens all across the Eastern seaboard at peace of mind, nevermind that their compatriots at Chicago are being systematically genocided by the hundreds of thousands, if not millions. And you call that "Reasonable mechanic"
You're interpreting happiness too literally, and I think you're not taking a fair level of abstraction.
What does Milistania do? They invest resources in maintaining public order. Yes, i think this is reasonable.
As it so happens the actual building names in-game are theaters and stadiums, but they could just as easily be dungeons and riot police and prison camps and surveillance state.
The game chooses to not have both sets (ie carrot and stick) because we only want one line of happiness buildings, and because the game has a general positive, upbeat vibe.