A point that was made in this thread, or maybe the other one, I'm not sure now,
@Chaosmancer made it, was that the base problem with Exploration as a pillar is that Exploration is almost never the actual goal. It's what you do on the way to the stuff that is actually the goal. So, right out of the gate, the stakes in Exploration is never really all that high. After all, if the DM is running you through the Deep Dungeon Of Dastardly Deeds, he's not likely going to kill your party on the way there. And, since the DM wants you to get to the Deep Dungeon of Dastardly Deeds, any challenge he throws in the way is likely pretty low stakes stuff that is largely throw away. Thus the whole Random Encounters tradition in D&D.
I have to admit though, the system in the OP intrigues me since it actually sets a goal and stakes right in the random encounter. There's actually a reason for engaging with that random encounter, instead of trying to either bypass it or get through it as fast as possible.