Taken to its logical conclusion, this suggests that rules are always playstyle agnostic.
But, they are not.
I think one can argue that5e, at least, doesn't really push you toward any of CaW, CaS, or CaT - other editions certainly did, but 5e manages to split the difference.
Early editions definitely favored Combat as War, by making actual fighting something you didn't want to do. It was brutal, expensive in terms of resources, and not directly rewarded. XP for gold is one of the main factors here - combat will cost you hit points (which were harder to recover) and skipping it didn't reduce your overall rewards. I'm not sure if this is fully intentional or just the only way Gary imagined the game being played.
4e was certainly deliberately written with a Combat as Sport playstyle in mind - the strong focus on balance really emphasizes this.
And while I suppose 5e does the most to support Combat as Theater, that's only because earlier editions did nothing. You need to look outside of DnD to find real mechanical support for CaT - Masks: A New Generation really goes all-in on the idea with several core mechanics (such as their attributes) that really lean into it.
You can, of course, play in an unintended style, but with 5e I don't think any of the three require fighting against the system itself. This may have even been the intent of the design team.