That explains the Wii U and Wii. Or the 3DS, DS, and GBA. Oh, right, no. Yes, it'd cost more to support older systems, but over time that old hardware becomes ridiculously cheap. PS2 on a chip and XBox on a chip could have been a real thing. Instead we saw PS2 support dropped and XBox done through emulation. Would BC have made the systems more expensive? Almost certainly because they kept changing core CPUs. Drastically more expensive? Probably not. I mean, the PS3 kept PS1 support.
Actually that really depends on the setup. Peripherals being emulated in software while having 99% of the hardware there is the most likely circumstance. Code injection is of course another possibility. Really it's up to the hardware designer to figure out how much they want to support in real hardware and how. For instance, the Wii U dropping the Gamecube controller and memory card slots was a cost cutting thing that dropped Gamecube BC to save money. It wasn't drastically more expensive. Nintendo simply chose it wasn't worth it to them to support it. Personally, I think that was a bad move.
adressing your first point: the PS3 was ridiculously expensive at launch, thats why they switched to partial emulation for the second batch, which made playing PS2 games a nightmare, then they switched to full emulation for the slims and super slims and you hack those 2 models you'll have much better results than with partial emulation, so it was either shit backwards compat or a 500 dollar console with a cheaper alternative, its not economically sound, the PS1 support in the other hand is emulation, therefore every model has it, same reason why every PSP can play PS1 games if converted to eboot, emulation is simply more flexible, same thing happened to the wii, the DS and the GBA, later models removed retrocompatibility because games for that older system just werent being released anymore and the hardware got cheaper because of that, even when the gameboy micro, DSi and wii family still have the internal hardware needed, which was a side effect of building the system around retrocompatibility, infact, the 3DS suffers the most because if this, you know how many processors the 3DS needs to run 3DS and DS games? 4, 4 fucking processors, you have the 3DS's own arm11 CPU and its graphics chip, the DS's arm9 and the GBA's arm7 which is required for DS games to work properly, every single 3DS model has them because its simply impossible to run 3DS software without the DS (DSi actually) processor and DS games cant be run without the GBA processor, which means that all 3 ARM CPUs are needed, its ridiculous and its the reason why a GBA VC on 3DS was never a thing, nintendo simply didnt want to bother emulating a system that already has nearly the whole thing inside it.
regarding your second point: dropping the gamecube ports was understandable on the wii u, the console was a decade+ old, so supporting hardware that they cant profit of would be silly and the market they were aiming for was the casual market, opposite of the wii, the OG wii had them to appease developers worried about the sales of their gamecube games, not for gamers, same with the GBA compat on the DS.
thats why i want emulation, because in most cases its an effort for the gamers (the exception being the horrible xbox emulation on x360, some games work fine but most work like hot garbage) or at least to appease a fanbase rather than companies, thats why the PS2 classics on PS4, as much of a dick move as they are, are pretty solid if you have the extra cash for them thanks to the achivements and good video output.