It's almost 2016. I don't think BC matters much to the typical console gamer to be quite honest.
It is nice to have, but has usually been problematic to some degree :
PS3 only some early units played PS2 games, and not all of them worked perfectly.
PS2 only the fats played PS1 games, and not all of them worked perfectly.
X360 only played a handful of OG Xbox games, not sure if any had issues.
X1 only plays select games, and they basically have to be downloaded/reinstalled due to the recompile. Some work great/better than original, while others have issues, and availability is sketchy title for title.
AFAIK Wii Gamecube emulation was pretty excellent, but I think that got dropped as well (or did they just drop the ports? Honestly I have no idea)
The best backwards compatible platform has been the PC for obvious reasons, but it also helps to know what you're doing, as much older games often need one or more things like DosBOX, DX9 optional download, GLide wrapper, widescreen patch, community patch, modified INI, custom shortcut (run in compatiblity mode and/or run as administrator), etc. It's easy when you know what you're doing and have reasonable google skills, but is daunting to less advanced users in many cases. But that's probably par for the course when you're talking ~30+ years of titles encompassing many MANY tens of thousands in total.
A hypothetical gen 9 Xbox and Playstation should definitely have BC, unless they decide to drop x86, or they change architecture and certain games utilize features that aren't a part of the new systems. One way this could happen is with Jaguar/GCN's version of asynchronous compute. AFAIK, it's virtually unused today, but I could see late-gen games using it to achieve the final pushes forward in maximizing gen8. If Gen9 uses something non GCN, then making the ACE code work with an altogether different implementation may not be possible in a feasible fashion.
In a way, that's the problem that faces PS4 in running PS3 stuff. The Cell was ludicrously sophisticated for the time, and we even saw benchmarks where in raw CPU ability the Cell 3.2Ghz wasn't very far off of the Jaguar CPU in the PS4. The way Cell worked was absolutely nothing like an x86 environment either, so emulation would take an inordinate amount of power to achieve unless the games were recompiled in such a way to run natively x86. Worse, the Cell was also often used to divide up the SPEs in order to help with graphics work, turning a difficult task in emulation into something that would take divine intervention to achieve.
We're getting into the meat of gen8 though, backwards compatibility might have meant a little in 2013, but 2016+, it's purely niche. There are simply too many major games hitting for many people to care about gen7 titles. And for anyone who really cares strongly about playing gen7 games, the best overall result will always be to play on gen7 consoles (that are plentiful and cheap, and I'd imagine most players with that much invested in gen7 will simply keep their console if interested).