IMO MS and Xbox are going generations-less because their main goal is not to sell consoles compared to PlayStation it's as Nadella says to reach as many people and get them to invest in their services and stay invested regardless of device they prefer. With Xcloud not yet ready for a full launch across many devices and also become a bridge for late adopters or devices not capable of running real next gen games the most sensible thing to do then is to not go all in on next gen and instead go their current path and only develop cross gen games for the time being at least both giving cloud infrastructure time to mature and keep as many people as possible able to play their games and keep on being subscribed to their services even on "old" devices.
Off course that don't mean they don't want to sell consoles and will be thrilled if you choose an XsX as your primary device but they will not feel sad if you instead consume their games and services on a PC, Phone or on your TV without even a console plugged into it if that becomes an option or probably even competing platforms and instead of their success being tied to hardware adoption of their own products become the Netflix of games as Nadella puts it.
So while it means they are not going head to head with Sony who's main goal instead is to transition people over to the new gen at an unprecedented pace investing in next gen only games to drive that transition that is just a side effect of following Nadella vision he set Xbox on and PlayStation having another.
Nadella vision for the whole of Microsoft and its services is to be available everywhere and just like how gmail is supported by outlook , how office is available on apple products I believe he would make Gamepass and Xcloud available on PS products the second Sony would let them.
The guy was thrilled to make PlayStation use and become their partner in developing cloud gaming on their azure platform and PlayStation equally thrilled to be a part of it.
These companies both Sony and Microsoft do what they believe is best and most profitable to their shareholders and if that is working together with companies competing in certain businesses areas it won't make any difference.
And while it means their games like you say will be available for more consumers day one with not being build around next gen hardware to me personally, and I bet a lot of other enthusiasts and early adopters of the new hardware, would rather want developers to create experiences not previous possible and getting the most out of the new hardware I put several hundred dollars on this is not "pro-consumer". While I am fine with a Halo with ray tracing and fast loading I can not stop thinking about what it could have been if it was not also developed with a "unusable" CPU as DF puts it themselves in a PC environment when speaking of the jaguar and a 40 times slower drive among the rest of the old hardware keeping innovation and creativity back.
And while I would have preferred MS going the "usual" route console manufacturers done and push next gen technologies and game development day one with Microsoft pushing services and cloud through their entire company it makes perfect sense for Xbox also having that as their main goal and thus this decision. I wouldn't be surprised if they keep supporting the one X with first party games even in a couple of years outside the big AAA ones.
PlayStation is pushing hardware adoption instead and while being a "hardware" centric company perhaps should be reason enough personally I believe they have two other very good reasons for doing so with PlayStation 5.
1: They already have managed to sell more than a 100 million PS4 and coupled with its services already being far more lucrative than even the PS2. Getting as many of those customers invest in the next console and continue to also invest in their services tied to it will keep that revenue stream going for another seven years or how long the next generation is is basically a no brainer and also because...
2: They believe cloud gaming is not "ready" yet and there is quite a lot of things pointing at that from both the performance of their own cloud service, the launch of Stadia and even from Phil Spencer himself saying it's not a replacement for local hardware yet and right now the phone in your pocket is what Xcloud will target.
You do remember that PS have had their cloud service up and running long before Xcloud was even mentioned by Xbox? And with PS also going forward able to use the same Azure servers as MS their is nothing stopping them from providing the exact same experience as any Xbox cloud platform or service should they want to invest more into that area than they currently are basically.
So for Sony to be "done" in six years they would not have to do a misstep they basically would need to go from mistake to mistakes year after year and never adapting to customer behavior while having the same cloud servers available and competing services already up and running (PSnow). This while having a far larger customer base from this generation already tied to their ecosystem both when it comes to retaining your digital library, backwards compatibility with discs among many other reasons to stay with them and compared to Xbox also being available and supported in (and completely dominant in several) far more markets makes this idea basically fan fiction.
I believe both will be tremendously successful next gen and reach even more "gamers" both than ever before and push gaming and technologies together in different ways and both have solid reasoning behind their strategies and while they differ there is nothing stopping either to adapt should the market point in a certain direction or the other.