Occasionally, Microsoft will decide that there is a mystical distinction between versions of its operating system, creating a scenario where a new version is the only one with the latest DirectX - what you might call "forward compatibility." But compatibility going the other way is something you don't consider on PCs. The only time I've ever had it become a serious problem was when my computer was now too good. And even that can be ameliorated.
What's sort of funny about the whole thing was that the original Xbox - gah, which I keep calling the Xbox One, and then correcting myself, and then lamenting the choice which I think is good on its own but more complicated in context, which balloons some conversations (like a lunch order at Wendy's) as much as four hundred percent. But! The original Xbox was a computer. It was a Pentium and an nVidia board bolted inside of a breadbox. There is an alternate universe out there where the Xbox was simply another Operating System, for another type of computer, existing in parallel with Windows, and of course your shit always works because why wouldn't it work. It seems like a cool universe! I'm just saying. Also, a snakes can learn martial arts there, which just seems like bad policy.
Being able to play games from the previous generation on a different console is an incredible bullet point on something you already want to buy, or an inducement for especially devoted fans, but this is an edge case for most people. Where it becomes elevated in importance is when we're talking about the kinds of digital libraries we're likely to amass in the next generation, where "backward compatibility" is the difference between having access to something and that thing ceasing to exist in a real way. People wonder, and not without reason, if this is the "last" console generation. It's certainly the last one that looks anything like the previous ones, and that's probably how it should be.
I buy consoles because I want to play new games; I don't have a "1984" on those systems that I go back to annually. This is much more important for a new player. I try to imagine how Gabriel's mom would respond if she got a new phone and then, if she wanted to use any of her old Apps, she would have to carry her old phone around too. What we think of as normal is, as has been said many times, actually sort of fucked.