The irony is that it's precisely when exploration started to become important in real History, at the Renaissance, that it loses all value in Civilization games. We can wonder why is it so?
In real History, it is the development of global trade which motivated Western European powers to discover the world. They needed to control distant outposts in order to secure trade. That's an aspect which has hardly ever been represented in the Civilization series, yet that's really what Empire building is all about.
It's not anything really new though, that's exactly what the Sumerians, the Egyptians, the Phoenicians, the Greeks and the Romans have done earlier, except that it was performed at a much larger scale. I see here a potential to extend the 4Xs for a much longer period of time, all through the game actually, rather than stopping midway in the game once all civilizations are established in their own corner of the map. Maybe late game boredom is explained precisely because there's no longer any of the 4Xs in action.
The discussion, at least as I understand it, is absolutely not about restricting one of the X's, it's the exact opposite actually.
There were some differences in the various Powers' versions of Exploration/Expansion, though.
Let's see if we can find a Common Thread:
1. Sumerians. The classic version of their expansion was in setting up distant settlements to exploit Resources - specifically, two small 'cities' in the mountains of eastern Anatolia to produce Copper and copper artifacts and ship them back to Uruk and other Sumerian cities. I suggest that the reason more of this isn't done at any time in Civ is that it requires ou to build a Settler, send it off (protected) and develop an entire City to gain access. Let's hold that thought.
2. Greeks and Phoenicians simply colonized - setting up new cities all across the Mediterranean, parts of the Atlantic Cast of Iberia and North Africa, and the coast of the Black Sea. This is pretty basic, classic 4x behavior: EXpansion at its most concentrated.
3. Romans didn't found so many new cities as they simply conquered existing cities and peoples and incorporated them. And Roman integration of other peoples with very different cultures into their Empire was so successful that Internal Revolt was almost unknown and not a major component of the final collapse of the Empire - a pretty remarkable achievement when you consider it.
4. Finally, note that while Europeans eventually conquered wherever they went, that was not universal: where they encountered established and powerful native States (India, China and East Asia) they more often started by establishing Factories - toeholds in major ports from which their Trade representatives could operate. Many of these became or were built as Fortified places, but for the most part they were not large or 'threatening' in themselves.
In all of these, the common thread is Trade. The Sumerians established their distant Settlements precisely to trade needed resources back to the homeland, trhe Greeks and Phoenicians had major trade networks with the colonies even when they had only ephemeral political control or even contact with them, the Roman Empire's wealth rested on massive trade networks that extended from Britain to Mesopotamia within and Scandinavia to India without the Empire. And, of course, the Age of Exploration could just as easily be called the Age of Exploitation as Europeans wove a net of Trading networks around gthe world.
So, I suggest that several things might be required to both put Exploration back in focus and also allow for the varieties of Exploration, Exploitation and Expansion represented by the 'historical examples' cited.
1. Allow a Civ to set up Smaller-Than-City, one tile 'bits' of Owned Territory. Need a resource that's 15 tiles from your nearest border? Use a Unit which is not destroyed in the process (perhaps even a single Action by a Builder?) to establish an Outpost or Settlement on the tile and gain access to any Resource there. Later, that same mechanic, perhaps using a Great Merchant, could establish a specific Fortified Trading Post next to or near a foreign city that funnels both Resources and Trade to you homeland, so that both the Age of Exploration Factory system and the earlier Outposts are covered by a similar mechanic in the game.
2. Perhaps 'lighten up' on the age-old requirement to build a relatively expensive Settler to found a new City. After all, Humankind goes much of their game without Settlers, and it would make it much easier to recreate the massive expansion of the Greeks and Pheonicians in the late Ancient/early Classical Eras. The downside, of course, is that many of these new cities started out Greek or Phoenician culturally, but almost none of them remained politically part of any homeland Greek or Phoenician political entity. Essentially, then, you would be starting new City States, perhaps with a distinctive set of characteristics related to your own Civ, but with no political loyalty to you.
That second would require, of course, a whole new set of definitions of in-game advantages. After all, at the moment it's hard to see why you'd want to set up new City States when you could, even with more effort, settle the same territory with a loyal, completely controlled new city of your Civ. Possibly this could revolve around Trade advantages with City States that, at least temporarily, Trump the advantages from having the city as a wholly-owned part of your Civ.