But it's not as though heat transfer only occurs when the cool air is outside the building.
But isn't that like saying that a hot roast put into a box will cool down if placed in the snow, but a pint of ice cream in the same box would not melt in placed out in the hot weather...? Entropy always occurs - molecules in an excited state (heat) will preferentially seek a non- excited state (cold).
All I know is that, even aside from entropy, I've spent some summers in non- or poorly-insualted places, and the walls felt hot, meaning, the AC had to work harder to overcome the huge numbers of excited molecules which are available to exchange their energy state with the preferred non-energetic/cool state. OTOH, a well-insualted place will not have warm or hot walls, or at least, they won't be *as* hot/warm.
WIndows are another matter - as I'd mentioned, we'd gotten replacement windows in the first house in Ontario, and in Winter, the windows were warmer to the touch than were teh walls, IOW the windows (and their frames) were better-insulated. In this place, teh windows are double- paned but they suck - a lot of heat-exchange occurs because the frames are single-layer aluminum. IOW, crap. Also very difficult and expensive to replace, because they are basically mortered into the brick.
I of course can't speak as to r-11 versus r-13, but given the cost of air conditioning, which ain't about to go down, given that most electricity is still generated by burning either coal or gas, is a little extra insulation THAT much of a "wasted expense"...? What are the long-term figures? I mean, some people thought we were nuts for "wasting" money on the tech shield, but the figures indicated that, in this climate, it'ds pay for itself in jsut a couple years.
I just don't think that extra insualtion is as pathetically stupid as the OP intimated by the tone of the post.