I don't think you can really say that engine size is irrelevant. I mean, if we want to pick absurd examples, how about a diesel ship's engine? It's only a few hundred tons, after all...
Smaller engines will have less mass to move, generally have fewer moving parts, generally have less coolant and oil to heat up, definitely have less engine to heat up, should have less internal friction, and so on. Calling all of that irrelevant is ignoring something that shouldn't be.
Remember that cars built for top MPG contests have little tiny motors. If engine size were truly irrelevant, at least some of the winners would have stonking big V8s.
Note that I am not saying that engine size is the only thing--heck, there's a good chance it's far down the list of what is important for fuel economy. But my contention is that it is on the list. "Irrelevant" says that it isn't on the list at all.
Confounding a simple analysis is the fact that different vehicles and use cases have different engine requirements. A 660cc engine in a minivan might very well work for puttering around in the city with a load of groceries in the back, but it's not going to cut it going up a mountain on the freeway. And, of course, the fact that most consumers want MOAR POWAH (so they can get their groceries to 60 MPH in less than five seconds?) which is easier to do with a bigger engine.
I agree with the analysis in the first post, that the gearing is one important cause of smaller engines not getting the kind of fuel economy numbers that we might expect. But, if my priority is to get good fuel economy, I will choose the smallest available engine option and try to find better gearing.
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