Because we like D&D? What can I say? I personally don't need mechanics and rules to help me explore/interact. The simplicity of using skill checks and narration works for me.
It's just a missed opportunity. I mean, I don't know about you, but I can have a fun RPG with zero mechanics. Dr Magnet hands is an AWESOME improv game with rules that fit on like, half a page. However, the players handbook runs to a couple of hundred pages of mechanics, then we have the DMG, the monster manual, a bunch of supplements, so we're sitting down to play a mechanically complex game.
Given that we're saying 'we're playing a mechanically complex game' you can do a lot more, and it's something that's sorely missing if D&D is not supposed to be a combat focused game. (I'd dispute this of course, I think D&D is a combat focused game so the very bland combat minigame is a huge issue).
Examples of cool mechanics that support other aspects of games are things like Apocalypse world for example has a mechanic where another player (the one you have the most history with) highlights one of your stats and the DM highlights one of your stats at the start of each session, and you get experience for using those stats. This is a great way of helping set up stories and really supports a storytelling game. If the GM wants to have a session about introverted psychological thinking, he can highlight the stat related to that. Everyone is encouraged to jump on board.
Now you're thinking 'I would just jump on board anyway' but this way you're rewarded so there is more buy in, it's flagged explicitly upfront, and because the PLAYERS get to highlight stats as well, they can also help shape the story (and because you can shape other characters story you can gently bring them along with things).
It's a really cool mechanic that helps let everyone shape the story that will be told. Bam! Mechanical support for storytelling in a very subtle way.
As for skill checks, mouseguard has a great system where it switches focus and complexity of resolution based on the meaningfulness of the task. If it's a minor conflict you just roll, but if it's a major conflict there is a more granular system. This is very useful in practice if you want to have exploration focused challenges because it lets you arbitrate, say, the difficulty of leading your caravan through the mountain pass and then the lost mines of whereever which is difficult in D&D.
Bam! Great mechanical support for crossing a mountain range.