Why isn't the application of "carb heat" in initial piston multi-engine failure emergency procedures? What is the rationale for not including the application of carb heat in the initial multi-engine airplane's engine failure procedure?

I've recently starting flying light multi-engine airplanes again and have been practicing the engine failure procedures. 

I noticed in the POH of the aircraft I'm flying that it doesn't mention applying Carb Heat to the dead engine. So I looked at some other multi-engine POH emergency procedures and noticed that Carb Heat is mentioned sometimes, but in the trouble shooting checklist for restarting, after the initial procedure. 

Shouldn't carb heat be applied as soon as possible, while manifold is still hot enough to heat the air to melt any potential carb ice?  Like immediately after pushing everything forward and getting gear and flaps up? 

Alternatively, I can also see an argument that before you identify the dead engine, applying carb heat to both engines would decrease some precious power from the currently functioning engine. Are there other reasons for not using carb heat sooner?
Partly because carb heat is ineffective once the engine is no longer making power, but mostly because the initial engine out procedure isn't intended as remedial action to get the engine running again; the drill is to make sure the airplane is configured to be able to climb (somewhat) in the moments after the failure, so the priority is everything balls to the wall, gear and flaps, identify, confirm, feather with the aim of establishing a climb foremost.  

In any case, if you applied carb heat to both engines as part of the drill, the dead engine would be getting probably insufficient heat anyway, and the live engine will enjoy a few percent power reduction from the application of heat.  On a piston twin like a Seminole or Duchess at gross on a hot day, that alone may be the difference between barely climbing or descending, so that the remaining engine takes you directly to the scene of the crash as the old joke goes.