And usually, the original developers aren't the ones developing the game for older hardware vs new hardware.
That was because previous gens had different architecture that required much more effort to do a port. This gen transition entices publishers to sell games that can be easily sold on both generations with just minor tweaks in graphics settings by the original dev team. Essentially the first few years of the upcoming generation is going to be just XSX and PS5 having games with some combination of higher res, higher lod, higher fps and maybe with some effects like reflections replaced with ray-traced equivalents. The games will still be otherwise designed around Jaguar limitations, so only the visuals are next gen, but nothing else. If design teams start building games next gen first and then want to make a port for old gen, they'll quickly realize it's not happening without compromising one or the other, and once money comes into the equation, publishers will insist that superficial "ray-traced visuals" are enough to sell "next gen", and devs are forced to design to old gen limitations primarily.
Third party certainly won't be doing any risky exclusives, other than maybe few indies trying out a low budget gimmick game to differentiate themselves. It's the job of the first party studios to push next gen, but MS's stance seems to be that XSX doesn't need such things, and that the superficial updates will be enough to sell their new console for the first year or two. This could be a huge mistake if Sony makes any compelling exclusives instead.
I do get where MS is coming from with this strategy. In reality, launch year exclusives are often not that special, and these days making a truly next gen experience is not going to be easy to fit into a launch year window. Personally I think they should still try to showcase what can't be done on previous gen, otherwise the selling points of the new console are pretty lackluster. I think there would be room for more experimental smaller games that couldn't be done on previous gen, but MS seems to still be lacking the studios to do such a thing, so they'd have to essentially pay smaller third parties to come up with such stuff, but that is not very feasible when we are talking about launch window titles.
In any case, I think MS and Sony have been rather lackluster with their first party ambitions. It feels like they're trying to make safe boring sequels that sell well, essentially the same thing that big third parties do. There's very little experimentation or pushing of new ideas, which is what I feel first party should be doing. Instead, it's just "let's make yet another third person cinematic action adventure" that's like the fast food burger everyone knows what it's about, with nothing truly surprising about it, just dressed up slightly prettier than before. It kinda misses the point of gaming vs. movies. They're not making better games, they're making games look more like movies while the actual gameplay doesn't evolve much at all.