I believe this desire is in fact a natural instinct of gamers, and one that most RPGs have catered to over the years. Such secrets, side quests, and optional distractions provided depth to a game world. This instinct often runs counter to another driving force within gamers--the desire to be able to make meaningful decisions that change the world or alter their course in a greater story.
It seems a classic problem to be caught between the two. There are games that allow the character to chose to be evil or good, and in some cases the choice feels superficial (Fable 1) where the choice affects your powers and meaningless NPC reaction, but does not alter the core story. There are games that allow the character to make choices that lead them down radically different paths throughout the game world (some of the Star Wars games)--truly branching the story. Future role playing games (the Mass Effect series) will develop this concept farther, allowing you to affect the world and its denizens in many ways, through active (directly making a choice) and passive choices (ignoring something that is happening elsewhere), brining computer gaming closer to pen and paper games, in which your ability to affect the world is paramount.
You could suggest that the answer lies in game replay. If the game is exciting and engaging enough, a player will be excited to play through the game a second time, trying the alternate courses and options until he or she has exhausted the entire world, even if it takes multiple runs.
Game play can be dry if you feel as if you are rail-roaded down a certain path. As a gamer--what is your preference? Would you rather follow a single story line and gain full access to the world in a single run, or have a real handle on changing the face of the world and your place in it, but in doing so, make certain alternative realities only accessible through replay?