What is the reason that will stop them making an APU die the size of a 7850 die, with the number of GCN cores that a 7770 has, paired with GDDR5 main memory?
First, you'd need ~64MB-128MB of eDRAM, on top of 7770 level GPU and the CPU, you are talking ~GTX 480 die size. How are you going to cool that in a console? You could say pairing GDDR5 with a 512bit bus would work giving up the need for eDRAM and getting it down to simply an enormous size die, but the production costs for the mobo and the cost of the RAM would end up being more then the cost of the APU. If the goal here is supposed to be saving money, a custom MIPS or POWER part with a dedicated GPU would be considerably cheaper then either of those setups, and it would rather handily best it in performance too.
Because I can't see any theoretical reason why APU performance would have to be inherently worse that CPU + GPU performance
There are two reasons that aren't theoretical, die size and memory throughput. Dedicated parts for each allows *significantly* more flexibility in terms of die considerations and having separate memory busses significantly reduces that bottleneck not to mention allowing you to have much larger cache on your CPU *and* eDRAM on your GPU. There are massive reasons that an APU can't best dedicated CPU+ dedicated GPU, the only reason APUs are ever viable is if they are "good enough". The problem with that mentality, if say MS decides to go with "good enough" and Sony decides to go with good, MS is going to be obliterated(the inverse is also true, just MS has a bit more history working with x86 vendors then Sony so I used them).
It's been pretty commonly mooted that both MS and Sony aren't looking for the same bleeding-edge tech that was in the 360 and PS3 at launch.
Sony's big expense at launch was their BluRay player. I'm not saying that it is reasonable for MS to release a console with a GPU a generation ahead of the PCs like they did last time, but thinking they are going to use a castrated two year old low-mid range product? Not seeing a lot of good logic to that.
Nintendo handily won the last round of the console war- don't you think that the other two teams are going to be stealing a few pages from their playbook?
Do you not follow the console market?
http://miami.cbslocal.com/2012/07/28/game-over-for-nintendo/
Nintendo's strategy was short sighted and doomed to fail from the start over the long haul. Everyone who follows the market knew that before they launched and it happened. Their tie rate is the lowest of this generation(which is where most of the profits from consoles normally derive), they have been forced to launch at least a year ahead of everyone else despite coming out last(barely), they also have gone from have ~55% of sales for the category to under 21%. Nintendo had a short term strategy last generation, and it worked.... in the short term.