Yeah, armor in real life works by having a blow hit "it" instead of "you" directly. The effect of strength seems pretty clear to me, from Society of Creative Anachronism examples. Still, there is some abstraction going on in terms of what a successful attack roll that reduces hit points means. High-level characters' hit points represent more than just literal ability to take a beating, including (per the AD&D DMG) magical protection.
The traditional D&D philosophy is that if the abstraction is too poor a model for a given case, then you substitute another model. Poison can kill regardless of hit points, and failing your saving throw means you looked at the gorgon ("medusa") and got petrified. You can't look at it if you're blind, but that might make fighting difficult.
The concept that the player, as a sort of author reaching down into the world, is using a power -- rather than a particular character in the world using it -- can go far to make something seem less magical. An author might still be concerned with the world's internal consistency, though.
The interaction in 4E of the storytelling game, the boardgame and the roleplaying game may seem awkward to some people, I think especially to those (such as me) accustomed to give the roleplaying aspect priority in D&D.
How many times do we have to point that, yes, Hippogriffs are magical beasts?
The trouble here with the "slippery slope" argument is that it's being used in defense of an avalanche!
It seems also to be a defense of rules-lawyering, which under the circumstances seems to me sensible. The 4E design would probably collapse if subjected to the "fluff-lawyering" that almost everywhere else is called "role-playing".
"Diagonal" measurements are no problem if one is not using a grid in the first place! (A hexagonal grid gives six directions, but also an artifact of staggering against the grain). Templates are nifty for cones, spheres, and so on. Dealing with a cross-section bisected by a floor takes a bit more, but that comes up very rarely in my experience.