I love when this argument is thrown out by some fans of 4e, who play a game with a million and 1 powers that, at least partially, codify combat and provide a discrete power for a vast number of combat actions, which they enjoy... yet for some reason cannot fathom why someone would want similar mechanical robustness in other areas of the game... this is what boggles my mind.
I mean technically you don't need those powers, but players have fun implementing their mechanical effect in the game during combat... why is it so hard to understand some people would like to have the same type of fun using the mechanics in other areas besides combat?
Actually I think giant.robot explained the logic quite succinctly. You NEED rules for conflict because something has to quantify how conflicting actions resolve in a reasonably objective way. Otherwise you're just playing an elaborate version of Cops and Robbers ("bang, bang! You're dead!"). There's no NEED to have such a set of rules for whether or not you can build a boat or bake a cake. In any case those kinds of actions are at most only indirectly contributing to conflict resolution, unless you subscribe to the theory that cake baking contests are a significant aspect of the game that warrants a whole subsystem like that.
No, you don't NEED powers, but that really isn't the point. You need some way to decide what cool combat maneuvers the players can do and how to resolve them because otherwise you just have no rules at all worth the name. You could simply use page 42 for everything, but given that it is already there as a fallback for whenever you want something outside the more specific rules you see that combat powers are simply a convenient way to arrange the game so that the typical types of things people will try have already been worked out.
Beyond that you have character background, skills, etc that can be used to define in general what sorts of things outside of combat which characters are good at. The thing is it need not be more precise than say background because "out of combat" covers a VAST array of possible situations which may or may not involve conflicts. The game could easily have subsystems for baking contests, wooing women, running a business, committing graft, building a temple, etc etc etc but for the vast majority of games 99% of those won't be used. Beyond that it is a lot less likely that a DM will want to use them as-is. Combat mechanics tend to be appropriate to all campaigns and settings. Other types of mechanics not so much.
And then there's the issue of the oft-cited down side, that once you codify something into a skill, feat, practice, whatever then you've essentially created a converse rule that says everyone who lacks that element on their character can't do said thing. This applies to combat as well, but in combat everyone has a lot of things they CAN do and they all generally lead to the same ends, so it really isn't a big deal. Out of combat that isn't true at all and thus you have roadblocks tossed in the way of the story like "Oh, Joe Dwarf doesn't have 'swim', so I can't really force the party to try to swim the rapids."
Personally I think there's a zone in there where some things that probably will come up pretty often, don't generally block progress if they can't be done, and are unlikely to need huge variation between settings CAN be given mechanics. I'm not sure what the amazing value of doing so is, but whatever.