I think it’s debatable whether what you are calling CaW here is actually CaW. The enemies in your CaW scenario sound a lot more sporting to me. They don’t do anything particularly warlike.
though it does make me think there’s a third playstyle that CaW and CaS dichotomy miss. It’s the combat as special forces and I think your description above fits this. Essentially you are special and the game is enemies are played in such a way to allow you to consistently punch above your weight via shock/awe/surprise/strategicalness/etc and since you are special the enemy doesn’t ever match you on strategy.
I think this is a common way to play the game and is what is getting confused for CaW by many.
I think you might be placing more emphasis on the "war" part of the analogy than the dichotomy requires to be a useful description of different styles of play. Ultimately, Combat-as-War vs Combat-as-Sport describes a difference in how encounters are approached on a metagame level, and how those differences emphasize different types of IC strategies and tactics, rather than whether the in-world content of those encounters resembles a military conflict.
In other words, a CaW game doesn't need to have anything "warlike" about it or the opponents--all that is required is an expectation that players can (and should try to) have their characters affect the difficulty of encounters before the encounters begin. The source of the challenge comes from finding strategies and tactics to win (or give oneself as large an advantage as possible) before the encounter even starts. CaW is "warlike" merely to the extent that it approaches conflict with Sun Tzu's advice in mind: "A victorious warrior wins first, and then goes to war, while a defeated warrior goes to war first, and then seeks to win." Critically, Combat-as-War generalizes that mindset to all sorts of conflict, including non-combat encounters. (More on CaW in non-combat encounters below.)
A CaS game, by contrast, is characterized by the opposite expectation, that encounter difficulty cannot be changed prior to the encounter, and that it is poor form for players to try. The encounters are faced in the manner that they are presented by the DM. The challenge in CaS comes primarily from finding in-combat tactics to maximize one's chance of success, or, if success isn't in doubt, to minimize one's use of resources. CaS is like a "sport" only to the extent that metaphorically the PCs show up to a "match" and fight the team fielded by the enemy. It may or may not be a "fair" fight, but any unfairness is determined by the relative strength of the two teams, not by pre-game efforts by one or both teams to skew the odds.
The descriptive value of the CaW/CaS dichotomy extends to non-combat encounters, which further reinforces that the "War" in the name is describing a mindset rather than armed conflict.
As an example, consider a high-stakes negotiation. In a CaW game the challenge of the negotiation would be making the opponent
want to accept the terms you are going to offer before even sitting down to the negotiation table. (If the PCs are the "purchaser" in the transaction, maybe that means giving the opponent a sudden and critical cashflow problem; if they're the "seller", maybe that means artificially driving up the perceived value of the goods/services on offer.) In a CaS game the challenge for the players would instead be finding the right things to say at the table to get the best deal (either to try to get ad hoc bonuses on any checks made to mechanically resolve the negotiation, or to try to use the most optimal skills if the encounter is being run as a formal skill challenge of some type).
As another non-combat example, consider an audience with a King. Is the expectation that the PCs show up to the audience and use RP and skills and abilities on the character sheet to try to get what they want (CaS)? Or is the expectation that before the audience the PCs try to (e.g.) co-opt members of the royal court to influence the king on their behalf (CaW)?
Because the CaW/CaS distinction focuses on expectations for how the players approach encounters, it doesn't have to be symmetrical with how the DM approaches encounters. Sure, the "symmetrical CaW" approach you've raised for discussion would work as a playstyle (and would indeed likely be comparatively lethal), but the Combat-as-War label has descriptive value even for asymetrical games where the players are focused on winning every encounter before the encounters even start, while the DM is focused on running a game where doing so is both possible and interesting. Sure, enemies not using the same tactics as the PCs sounds artificial in a vacuum, but at the table a skilled CaW DM can make it seem organic, just as a skilled CaS DM can make a series of tightly balanced encounters seem organic.