Lately when I crank it in the morning after it's sat overnight the car idles roughly...not violently, but noticeably.

Clogged injectors? Dirty air filter?

 

seafoam it, and maybe you need new plugs, you buy the spray seafoam and spray straight into the throttle body, and the liquid can and have the engine suck it up, pour into the gas tank, combo of both

 

IACV: if the RPM is jumping....
PCV: if Rough Starts but can also lead to IACV.

 

on startup, rough is a designed feature. Nothing wrong.

It needs misfire to heat up the CAT.

 

Where did you Hear that?
Missfire is a very bad Thing it cannot be by default....

Our car Heats up the CAT by Closing the Loop A/F Ratio.

 

Yes they can, our cars miss (no spark is sent so fuel goes into cat warming it quickly)

Also newer cars will "misfire" when the fuel level is too low to alert the driver. And some engines with CVTs will "misfire" to simulate gear change.

 

google a bit and you know what I mean.

The misfire is less than 2% and won't trigger CEL.

 

our rough idle is often the EGR system is clogging and ready for its diy cleaning of the intake manifold,,,every 75kmiles its due

CK PCV valve in rear valve cover for free movement of ball inside

do Seafoam thru gas tank to get the injectors and fuel system
1 16oz can to 8 gal fuel - just under half tank
do that twice and its better than manifold vac method (which is instant cleaner for many parts and worth doing) but you can do it all thru gas twice if nervous

Plus clean throttle body air plate

ck air filter

how are the plugs? age/miles?