I'm expecting cross-gen development to be the norm (at least for third-parties) for at least a year or two after next-gen consoles are introduced, much as it was this gen.
I can see it working differently on Xbox/PlayStation, though - for PS5 you'll probably see traditional cross-gen ports, with there being separate PS4 and PS5 versions of games available. On Xbox I'm expecting MS to require UWP development so that there's one game that just scales across generations.
It won't be mandated, though - if the CPU improvements are anywhere close to the level we're all hoping for, MS/Sony will want to be able to have exclusives to show off what the system can really do.
Actually, thinking about it, it'll be interesting to see how MS handle retail packaging for cross-gen games, if they do stick to a single scaling codebase across generations - do they just sell one version of the game, and have it download whatever assets/updates as necessary on the new console? They could maybe bill it as some kind of "enhanced backwards compatibility", or something, but that would then make the library of games built for the new system seem smaller, which probably isn't a good look when an uninformed potential customer is looking at the shelves in GameStop.
Or do they sell separate versions in the respective case styles for the XB1 and the new system, even if there's no fundamental difference (aside from optional asset packs) once installed?
And how will the X fit in? It should be able to read UHD discs, which next gen games will presumably be shipping on (since BD is looking small even for current-gen games), and could definitely use at least some of the higher-res assets, so maybe they ship copies on BD in regular Xbox One packaging for the One/S, but ship UHD copies complete with asset packs in next-gen packaging, but have a "Works on Xbox One X" banner for cross-gen-compatible games?