Fanaelialae
Legend
I would say that in most typical CaW scenarios, the PCs are the agressors, while the enemy is the defender. Offense is easier than defense. The PCs only need to find and exploit one weak point in the enemy's defenses, whereas the enemy must try to defend themselves against potentially unlimited and unknown threats (using only limited resources).Claim: If the enemies ever adopted a true combat as war mindset then the PC's would eventually be crushed. This does not happen. Therefore, the enemies do not treat combat as War. There's something that seem inherently unfair about that and yet many still find Combat as War fun.
Discuss!
This mirrors the asymmetrical nature of CaW. The PCs need to find a way to win against forces that they could not necessarily overcome by direct means. The enemy puts obstacles in the way (traps, large patrols, etc) to try to block such attempts, but since they usually don't know when or where or how the PCs will strike, and in many cases won't know what the PCs are capable of, these generic defenses will generally be less ideal for the scenario than the players' custom tailored plan.
Of course, there may be some situations where the players have to assume the role of defense. Perhaps they've made themselves a sufficient nuisance that the BBEG puts a bounty on their heads. Even then, some consideration should arguably be made towards the PCs. It's not a bad idea to telegraph the threat, for example (maybe one of the PCs' allies hears about the bounty and informs them).
I mean, you could have the archmage BBEG scry their location, teleport over their camp while they're resting, and drop a meteor swarm on them. However, particularly for a low level party, it probably won't be much fun. It's essentially TPK by DM fiat, which arguably isn't really what CaW is about, IMO.
Ultimately, while I think CaW/CaS is useful terminology for discussing different playstyles, I do think it is often taken to extremes. I see it as a range. I doubt that most games are "pure" CaW or CaS. As the OP states, in a hypothetical pure CaW game, where the DM is antagonist and playing the enemy as effectively as possible, the PCs arguably don't stand a chance. And I find it hard to imagine a pure CaS game where the PCs meet Asmodeus at level 1 and Asmodeus is therefore a low level monster that the PCs can beat with only a modicum of effort.
You can have a game that leans toward CaS (where most combats are fair and balanced) but also includes elements of CaW (some encounters are dangerous or impossible to beat in a straight fight, and must be overcome by alternate means). I'd say that's my preferred type of campaign both for running and playing in. I similarly see no reason why a CaW style game couldn't utilize CaS encounter design for at least some encounters (particularly those where the DM is playing offense).