It's a trite statement to call Microsoft a software company and Sony a hardware company, but there is something to viewing this discussion through that kind of ideological lens. BC is where Microsoft's advantages as one of the world's most powerful software companies allows them to outperform Sony in a battlefield that Sony doesn't want to expend the cost to fight on. If we use this lens we can see where Microsoft might inherently view software as hardware independent because that's their ultimate model for Windows and everything else. Sony sees it all tied to the hardware because that's what they can control most easily. It's a fun ideological gambit by Microsoft that they can ultimately make Xbox into something that you just get a new revision of every so often and still can play all the stuff on. Not dumping the old hardware install base and offering GamePass services gives the impression that they're pumping value into their hardware for down the road when that won't actually be the case, it's a win-win for those of us who do want to always play that old stuff and Microsoft even if most people will just upgrade anyway.
The original Xbox One pitch was almost 180 degrees opposite from this, Microsoft wanted the Xbox One to be the center of everything, now they want the Xbox to just be another addition to your TV setup almost on the sly. Where you're like "okay, I've got Netflix setup and Disney+ setup, now I need to setup Xbox (Live) for games" and then you get the hardware for that rather than buying the hardware and then hopping into the ecosystems down the road. Microsoft is arguably faster to realize the software possibilities even when and where they fail and discard them.
Sony, by contrast, still seems to view the PlayStation venture as ultimately something that will sit at the center of your entertainment. It makes plenty of sense because the PS2 got there as a DVD player and a games player. But they still see the hardware as the key thing and they're less willing than Microsoft to simply eat the costs on the hardware to push the software. (Ironic considering this is what Sony famously did to both Nintendo and Sega!) This factors into the BC discussion because Sony sees each generation as separate because I assume they ideologically look at the specific hardware first and Microsoft much more easily sees the "software" sitting on top of all that hardware. Sony, if we apply this lens, would feel it's a waste to chase old and outdated hardware for fringe profits when they can push the newest hardware, Microsoft sees the potential advantages from having all that software available like software is available on Windows and especially the ability to sell it again for fringe profits.
As for exclusives, Microsoft has always gone through droughts where it loses the first-party push before going on a binge, buying up a bunch of developers, and "committing" to a round of releases just to let the developers "slack off" on Microsoft's dime. I'm not talking about just their Xbox stuff, look at Microsoft in the PC gaming sphere too, before Xbox even, they had this cycle ever since Ed Fries left. Hell, they had it with Ed Fries on PC. I think it's a factor of that "slacking off" which doesn't actually happen but because these developers no longer have the outside pressures, the standard time tables of getting releases out every two to three years slips and slips. And then when Microsoft has a corporate directive like "cancel everything on PC we're starting Xbox" or "cancel everything we're doing sports" or "cancel sports we're doing the 360" it creates another void and pushes things out further. I'd like to think that Xbox Games Studio is simply too large for this now, especially with Bethesda added, so we can have the best of both worlds in terms of Microsoft funding and quality releases at a good time table for PC/Xbox.
