My solution to the whole exploration problem goes in the opposite direction-- don't focus on game mechanics, focus on narrative. On description. On ideas. I mean that's pretty much what we already do... but I think we then get so hung up on trying "gamify" those ideas that they supplant the actual usefulness of just describing what is happening out in the world and letting the players think of ideas to get around or use those things, no dice rolls necessarily being necessary.
You describe to your players that they are approaching a fast-moving river... how the trees cover a lot of the area around it, the river being a certain width wide, the rapids flowing over the rocks many of which are sticking up out of the water sharp and deadly were you to hit them, a large tree trunk currently spanning one section of the river allowing the party to cross. A complete narrative description of the situation. No die rolls needed.
What happens now? Well, normally the players will start coming up with ideas on how best to cross the river. They will think of narrative ideas that make sense for this scenario, they may start flipping through their character sheets to see if they have anything written on them that will trigger additional ideas on getting across the river. All of those are great! I think that's what we want! Yes, at a certain character level they might be able to "fly" across the river because they have "powerful spells"... but so what? That's the idea the players came up with! They determined they had the magic available to make it across this scenario-- weighed the cost of spending the spell slot(s) against the possibilities that might have come from failure-- and all agreed together on their idea for "solving" this narrative puzzle.
So why does this situation need "mechanical support"? Does having some set of "game mechanics" to insert into this scenario actually make this scene better or more interesting? Would this scene be improved with the DM saying "Okay! Skill challenge time! Give me your ideas on how to get across the river and make a skill check connected to them... four successes before three fails and you make it across!"... thereby completely removing the players from imagining themselves within the scenario to now purely thinking of things in game terms? Figure out their best skill checks and then jerry-rig a reason to align that check to the scenario at hand? Or if not a Skill Challenge, then the DM inserting the rules of a "Hazard" that has been given to us, written up in the DMG, which essentially gives us the same thing as a skill challenge-- identifying a series of skill checks to pass that theoretically make sense for a generic solving of this issue, but do not in any way, shape or form align to the actual narrative the DM described of the scene, nor the ideas the players come up with. The "Raging River" Hazard says the group has to do X, Y, and Z to complete the challenge and the DM has to "force" those X, Y, and Z bits into the situation even if the players make no mention of those ideas because that's the "mechanical expression" of this Hazard the game has given us.
This kind of thing is exactly why I find all the complaints about requiring "DM Adjudication" to be missing the point. Because DM Adjudication is what created this scenario in the first place... DM Adjudication described all the incidents and issues the scenario presents... DM Adjudication is what will take the ideas the players come up with and then create mechanics on the spot to determine how good those ideas were... DM Adjudication is listening to your players and reacting to what they do. There's no random chart to roll on, no pre-written list of skill checks to follow, no paragraphs giving the DM all the ways to circumvent the use of magic the players might use to try and "solve" this scenario. Instead it's just presenting the scenario, listening to their ideas on how to get past it, maybe rolling a couple checks directly related to the ideas they throw out if necessary... and then you move on. The characters make it across the river, or maybe one falls into the rapids and starts getting pulled down the river forcing the rest of the team to go chasing after them. And then the DM Adjudication starts all over again (rather than the DM needing to grab some random book that has the "PC being dragged down the river" hazard listed out with the five mechanics skill checks players have to do to rescue the other one.)
While I understand that having lists of hazards or traps or other "game rules" are good at helping teach DMs how a scene like this could play out and the mechanics that could be used to solve these situations... I really think it's better if that's all they are-- just examples for teaching purposes. And that the DM should merely understand conceptually what they are meant to do, but are not proscriptive in how to do it. But rather they should use their DM Adjudication to run these scenes and scenarios on their own by reacting to what the players do and then coming up with their own ideas of what happens next. After all... coming up with ideas is the hallmark of this game... so to me, anything we can do to facilitate players and DMs actually getting to do that by bouncing off each other is always going to be the most enjoyable and successful way to go.
