BC would be the worst thing to happen to the NX in terms of hardware development. It's been hampering Nintendo since Gamecube. x86 has left everything else in the dust. Time to leave that ancient PPC750 behind.
Fortunately Wii and Wii U are not that powerful, so they could be emulated rather easily in something like XBO/PS4 and beyond.
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Don't forget PS2 hardware in the PS3 is also at least half responsible for the miserable PS3 launch ($599). The first PS3 motherboard was massive. Software emulation too was removed later as well due to the complexities involved in those non standard architectures. Don't recall the reason. Probably because those two systems are so unconventional that each game required case by case tweaking and it just wasn't worth the effort? Mind you they still sold PSOne and PS2 for <= $100 well into each succeeding generation so that is a factor as well.
But probably because they realized they could re-sell you your old games just like Nintendo as intangible virtual nothings. Hows that for "online capabilities"? Lol.
But ultimately the death of backward compatibility is online connectivity and e-shops. There's money to be had re-selling old games as virtual downloads. There's nothing to be had giving away a free emulator to let people play their old games, that would be completely defeating the purpose behind the push to all digital in the first place. No coincidence that PS2 compatibility and Gamecube compatibility were inexplicably and immediately removed once e-shops became a thing.
I'm honestly surprised Microsoft of all companies is trying to provide backward compatibility for free. You'd think they would be the first to throw them up on a virtual store and re-sell them to you. Desperation has it's perks I guess. I'm equally surprised that PS4 will let you play PS1 games even, because those are huge on the the PS Store, as well as Sony pushing PS Now hard.
I'm both a programmer and amateur VHDL engineer, so I know the effort and cost of maintaining backward compatibility in hardware, and doing things like removing Cell from PS3 or the Z80 SOC from the GBA has a tremendous cost and consolidation trade-off, so it's not ALL a digital downloads conspiracy. Just partly.
You also have consideration that most people interested in new generation don't really want to play their old games. At the start of 8th generation, everybody was completely DONE with the sub 720p shiny playdoh look of PS360 games after 10 years and wanted 1080p. Backward compatibility on XBO then in consideration of that fact is really just a "we have something you don't" tick box in a desperate losing battle honestly. I personally don't care, I still have a 360.
Then there are HD remasters. Publishers can make more money selling you the game again as an HD remaster, and most people with money in a new console and new TV would rather play the remastered 1080p game.
Software emulation is the way to go if you have the power leap. Even the PS2 with native hardware PS1 SOC as it's I/O and a/v codec co-processor can't quite play PS1 games without glitching and massive frame rate consistency problems. Plus you can patch on a game by game basis and ensure QA and stuff that you cannot do once your ASICs are in the store.
But I don't think that kind of demand is there from the user base. It's only popular on Xbox because it's something the other team doesn't have, that's all. I can realistically see a Xbox apologists toting how awesome backward compatibility is with 360 but guess what they are playing the awesome 1080p HD XBO re-release of a game and not the blurry over specular highlighted playdoh emulated 360 version! Microsoft as a software company is going to have a better time at writing software emulation but count me among those who would rather play the HD remaster or play a game on it's native hardware. I play my old 4:3 480p and below games on a Sony PVM CRT in RGB even.
Anyway...
If the NX is PPC7xx based in order to maintain backward compatibility with Gamecube/Wii/WiiU at the instruction level, it won't have a chance in hell at competing with PS4/XBO. Since that's what people, mostly PS4/XBO owners who aren't interested in Nintendo games in the first place, think they want out of the next Nintendo console, it would kill it before it launched.