"Rough idle" is a bit subjective without like a video or something, I'd say these 2.4 engines have a very rough idle but that doesn't mean we are talking about and experiencing the same thing. The engine certainly lacks refinement, balance, and isolation in my opinion but that still doesn't mean whatever you have is normal. Engine and transmission mounts need to be checked, if those are OK then its probably fine because the car would know and throw a check engine light if it was misfiring or anything like that. It might chalk up to something like "this is what happens when the computer tunes it to the absolute bare minimum amount of fuel and revs to keep the engine alive". Or in other words, rough idle maybe = less fuel used when idling. Don't know for sure, just guessing.
When mine is idling it will cause the steering wheel to quiver and the zippers on my backback in the passenger seat will wiggle and chatter, the passenger headrest will be visibly shaking... pretty strange considering all the effort they put into nonsense like an insulated double-wall oil pan but I'm at 34k miles of this now and its still driving just fine.
Its a little bit smoother than my other car I sometimes drive to work, which has a carbureted three cylinder motor. You want to talk about rough idle, that three cylinder from the 80s takes the cake for sure! Alas these 2.4 motors are super el cheapo mass produced things. You probably notice the roughness especially if your previous car was a Honda, now they have some smooth, well-isolated engines in their cars...
Wow that is interesting. Mine is super smooth, so much that when I stop at a traffic light I sometimes need to check if start/stop turned the engine off. I cant really feel if the engine is running or not if there is enough background noise to block the engine noise. But maybe it is specific to some cars car/engines since in my case start stop also turns the engine on/off without any shaking, which is something a lot of people complain about. I agree that since it is a greatly mass produced engine that is also fairly complex, there likely is some variation among units.