An APU includes memory and PCB complexity. Cooling doesn't cost that much. The Scorpio is smaller than the original XBO and comes in a much smaller box for instance so cooling can reduce size.
You couldn't be more wrong, i'm afraid.
The APU will include a memory interface, but a 25% faster GPU will need roughly 25% more memory bandwidth, which may be the difference between a 256bit bus and a 384bit, which requires more die area, thus bigger APU die, as well as more GDDR6 memory chips... potentially.
The PCB is the printed circuit board, so quite how the APU can include that as per your claim is clearly absurd. The point is a faster APU needing a bigger memory bus and thus more chips increases the board complexity and thus assembly costs.
Your cooling costs claim while technically true, the cost increments aren't insignificant and together with everything else will all add up.
Also, we're assuming a similar cooling system design in both cases, so going with a 25% faster chip that has to dissipate possibly more than 25% more heat (because increase in TDP with clocks and thus voltage is not linear) won't result in a smaller box assuming both cases use a similar vapour chamber heatsink as in the XB1X.
Dissipating a higher TDP requires more fin area and likely a higher air flow through the chasis; so for the same acoustic profile you can't escape a bigger box.
Honestly, assuming AMD hasn't really changed the arch to address whatever was bottlenecking their performance (maybe it was the FE that couldn't keep the SEs fed, maybe it was a limitation inherent to the SE design plus being bound to 4 SEs, maybe it was the ROPs, I've read several theories on what could be happening), I can't see either company, Sony or MS, going above 56CUs - it's literally wasted silicon for most purposes, actual perf gain above that being minimal.
I think Radeon 7 proves the diminishing returns between Vega 56 and Vega 64 are down to an issue of memory bandwidth.
That said, NVidia seems to need less bandwidth for the same performance and less for more performance most cases than AMD.