[CorollaMaster]

A slimmer tire also doesn't necessarily mean less sidewall flex, as it could just be concentrated into a smaller area.

Wouldn't that mean that less of the sidewall is flexing if its in a smaller area?

In addition, the amount of surface area that the power is being put into by the engine definitely effects the gas mileage. While the contact patch isn't solely responsible for rolling resistance, which I agree has a lot of different factors that add to it from what I've been reading (rotational inertia, design pattern of tread, skinniness of the tire, etc), it is definitely still very important to factor in. Unfortunately as you said, its not a perfect world with tires that don't deform.