AbdulAlhazred
Legend
No, you are confused. Whether or not the action is initiated by the player isn't the test. The test is how reliant the player is on an obstacle being present in the setting that the DM has made relevant to the skill and the DM's level of detail and support in resolving the proposition. Checking for traps is a very much classic case of a passive use of skill. Whether it is of any use at all depends on whether or not there are traps in the environment. Ancient Greek may be a very useful skill, but only if all the clues are written in Ancient Greek. Checking for traps grants you no reliable narrative force.* Being able to place a trap in the environment on the other hand would.
*(In fact, the opposite is often the case. If the DM is prone to improvisation, you are more likely to lose narrative force than gain it by checking for traps.)
Because it has no mechanical force, it remains a passive skill. If the rules elaborated, "In any wilderness setting, a player can make a Nature roll during every short rest to find level x 100 g.p. worth of useful reagents. These reagents can used to pay the cost of a ritual.", then the skill would have an active component that doesn't depend (very greatly) on encounter design or DM fiat. The very vagueness of what 4e skills do that you praise is what makes them so passive by default. Sure, a DM can empower them via consistent rulings, but since the rules themselves don't describe how to do this in detail and that's highly dependent on improvisation (which is never reliable IMO), they are likely to remain passive. Compare the treatment given to class abilities and the very definite mechanical benefits that derive there from, and a hypothetical treatment where Fighters had no class abilities but a combat 'knack' or 'skill' described in the rules only as, "Knowledgeable regarding combat techniques, fighting styles, and the use of arms." In theory, such a skill could completely substitute for all the class powers and maneuvers of a fighter and then some in the hands of a capable and flexible DM, but in practice it probably wouldn't. Likewise, in practice if it did, these 'rulings' would have a tendency to morph in to reliable and established house rules.
Sub-categories of Athletics doesn't increase its active nature in and of itself. But you'd have to bundle all possible benefits of various skills into Athletics to make it equivalently active. Compare 4e Athletics with my approach. For example, I have a 'Paladin' PC in the current group that has a 40' move purely because he's skilled at running, with no recourse to class features at all.
But if you think about it, basically every ability a character has is reliant on some sort of challenge being present. You can't fight if there isn't an orc to kill any more than you can't track if there isn't an orc to track. You may be able to define a rough scale that says "this ability is more often employable in a range of situations than this other one is" so OK, 'Streetwise' is more niche than 'Melee Basic Attack' in some sense. The thing is, the game is always give and take where the GM presents some material and the players react to it, and back and forth. The players may present some desire they have which is unprovoked, "I want to build a castle" but there is a heavy element of it being just a reordering of the normal presentation, because the GM will still immediately be tasked with indicating how, where, when, and if said castle can be built and any checks required to build it might come into play.
The only way to make the character's abilities truly 'active' is to give them authorial power so that the player of the barbarian can say "Grom is going to kill the huge ogre that just came through the door" and have the huge ogre appear in the narrative. There are games that do this, but D&D just isn't one of them. Players actions are always FUNDAMENTALLY reactive in a GM-centered game. I'm not really sure why 'active abilities' in a D&D-style game would be possible or desirable personally. I'm great with player initiative, and I run games that allow player narrative contribution sometimes, but I've actually found my D&D players don't LIKE it that much.