i think the primary reasons exploration fails in modern play is because it's tied up in a whole group of mechanics that are consistently ignored, rendered obsolete by other mechanics or just plain lacking: encumberance, food management, environmental hazards/weather and mapping.
exploration is about getting from location A to location B without dying on the way from starvation, monsters, diseases, 'falling off a cliff' or exposure to the elements,
correct me if i'm wrong but most people don't use any kind of distance map while travelling, the terrain is abstract challenge rather than concrete distance, oh sure the GM might look at the environment and say 'oh we're going through the swamp i'll throw in some apropriate challenges' but at most what'll happen is the trip boils down to a few battles against random monster or bandit encounters, but in previous editions it'd be a much bigger decision point: do we have enough supplies, there's no source of fresh water in there are we carrying enough, is it worth spending the extra days to go around the swamp for more safety, but spending more days meant that your food had to last longer and you had more chances to get lost which would cut into your food even more and if you didn't make your foraging check oh no we're all starving and have exhaustion
i think exploration could be improved by substituting encumberance's resource management for places of sanctuary, now what you're counting against is your finite class resources, without anywhere to long rest between locations every spell cast is permanently one less until you find safety, goodberries and create water chip away at your slots, do you cast tiny hut for a safe short rest or conserve the slot and risk a random encounter, your frontliners have taken a beating and are low on hit dice-best avoid that gobin cave even if you can see the fat stacks of treasure in the back, why cast fly or spiderclimb when your rogue or ranger can make an athletics check to climb the cliff and drop a rope down.