As someone who was present for the original CaW vs CaS thread, I think some historical context has been lost. It was originally part of the 4e edition war, where many felt the came had gone too far into narrative computer game simulations, and this was a well thought out explanation of why some people couldn't get behind the 'new' system (though perhaps a trifle unfair to 4e imho).
In the original definition CaW, more on DM adjudication was required, not less. This was due to the gritty, off book, or sometimes even silly, strategies and methods players in this mode would come up with that needed DM interpretation to apply to a more loose rule set. It was more about the social contract of what type of game the DM and the players wanted, how well the players met the DM expectation of what was appropriate and/or clever. Sure, most examples where from older editions were the rules themselves were less forgiving and therefore this style is perceived as more 'gritty,' but that does not necessarily have to be the case.
Furthermore, one could argue that CaS requires less "DM thumb on the scale" because the system itself (for systems designed to accommodate it, as the last couple of editions have been, I would argue) does that already by being "balanced" (for some definition of balance). Not that DM fudging can't or doesn't take place in CaS, rules only get you so far.
As for CaT, that is an interesting notion, and I think either previous style could be bent in that direction.