Curiously, measuring character skill is not something I am interested in an rpg.
I'm not sure why. The point of the game is to simulate a fictional world where fictional people live and see what happens to them when put into certain situations. It isn't to see how said fictional person would fare given the entire knowledge pool of some guy from modern day Earth. Plus, if all you are doing is testing player skill then you are entirely negating the physical abilities of the fictional characters.
A player can come up with a plan to roll underneath the blades as they swing(which may be easy or hard depending on the player and the situation). It might not be so easy for the fictional character to actually make that roll if he's extremely overweight and laden with armor.
The game is a combination of player skill and character skill. We test both of them.
3) To change the way that the game is played over time so that you don't find yourself doing the same thing and having the exact same style of campaign at 15th or 30th level that you had at 1st or 5th.
That last one in particular makes me wonder why 4e has character advancement at all, since 'the math' is actually designed to keep it from happening.
The point is that the story changes, the mechanics of what you do change, but the difficulty of facing similar foes does not. You get new options, which change the details of what you can do, you get more powerful in comparison to foes that you've already fought but you now face new enemies who are more powerful.
This allows you to make the progression from Heroic(local threats that only cause problems for a single village or city) to Paragon(regional threats that cause problems for multiple cities, an entire country, or a group of countries) to Epic(world wide threats to universe wide threats).
Your chance to hit against enemies who are equal to your level doesn't go up or down, but you fight gods instead of orcs and you teleport enemies to hell and back instead of shooting fire from your hands.
If you are supposed to win, if winning is the expected result, is it really a challenge or is it really just the illusion of success?
Winning is the expected result, but it isn't the only one. It's the same thing that happens when I sit down to watch a movie. 99% of all movies are going to have the happy ending where the heroes defeat the bad guys and everything is solved. That doesn't mean I should stop watching movies simply because I already know how it is going to turn out. Instead, I continue to watch them because I want to know HOW they win, laugh at the amusing lines of dialogue, see the cool scene where the hero blows up the building, find out the hidden secret behind the evil guys plot and so on.