Gee, I missed a lot over the weekend.
On human agency for smoothing out resolution, you guys already have discussed that it is a double-edged sword, but I don't think anyone has addressed exactly just how much so. Rather than tackle it head on, let me make an unsupported assumption (too generalized for purposes of illustration).
There are two types of DMs (and players to a lesser extent):
1. Those that already know how things work, to a certain degree, and thus fit the rules into that.
2. Those that rely on the rules to tell them how things work, and thus fit reality into that.
The example was an axe, because we assume that everyone knows how an axe works. Maybe they do, but I'm not so sure given the repeated incidents of reports of teenagers that don't know that hamburger comes from cows. I
know some of these people have never used an axe, and if they have even seen one, it was probably in a bad horror movie (held inexpertly). We can quibble about the depths of ignorance on axes, and I doubt many interested in gaming are that dense. Still, you've got people that think a war axe looks like the illustration in a gaming book, is held like human warrior in the picture holds it, and is a great tool for cutting down a tree. It isn't, though, because the handle is too short. (I know this because I have cut down trees with an axe, BTW.)
Thus are born the idea that katanas are inherently superior, and the oft-repeated request to chop through a 2" thick solid oak, bound door with a sword, without damaging the weapon. Most of us know there are limits to what a sword can do to a door (pretty severe ones if we are at all realistic). If we allow it, we allow it because the particular game we are running is ok with it--it's a highly magical sword, it's only mere wood, why not? Or some such.
And this is nothing compared to what magic can do. Magic that tunnels through dirt or even granite, leaving a (safe) passage? Magic that changes shape, and what powers and skills go with it?
The problem with the "tool" idea of explaining gaming, though, is that you cannot explain all possible tools in a way that will get through some of those mental blocks that think that cows and hamburger have no relation. Or you can to a certain extent, but the game can't
teach you about reality, and how the game differs from it. At best, it can try to convey to you what the reality of the game world is, in a consistent manner, and hope that your own slant on how this differs from the reality in your head will not cause too much trouble.
That is, it is not reasonable to ask a game to tell you how weapons would really work, and then also tell you how they work in the game. Frequently, the game authors themselves don't really know, because the game is based on ... film, literature, etc.
All our theoretical game could do on this question, if it wanted to be brutally honest, is have a several passages supporting this kind of thought: "Here are some weapons. Some of them might be useful in other ways. Depending upon how fantastical you want to make the world, some of the real limits might not even apply. We aren't going to tell you if a war axe is good for chopping down a tree, or if a magic sword can cut through a door, or if you can tie a rope to an arrow and shoot in a way that it can be climbed. That is up to you to decide. If you want to be more realistic about it, you'll need to educate yourself."
Edit: Any student of older fantasy literature can tell you that this question predates fantasy roleplaying. It is not entirely inaccurate to say that fantasy writers also divided into those same two camps: Those that studied fencing or other weapons so that their characters could act in plausible ways, and those that didn't care. There were some sharp words exchanged about it.
