On the other hand, having a living ecosystem in a dead cave makes much less sense. Some level of realism (along with how much more interesting the real world can be than
randomly generated dungeons) is why I want this in the first place. And the fact that Mammoth Cave is long stretches of passageway between rooms just means that you treat it somewhat like wilderness travel.
I certainly applaud the sentiment. My family was cavers so I grew up in them, and it does inform how I dress natural passageways in my gaming.
There are many fantasy caves though are not much like real caves. In fantasy, mushrooms aren't decay vectors that remove energy from the environment, but basic energy creators that support living ecosystems without the need of energy imported from outside the cave environment. Real cave environments of course entirely depend on transport of organic material into the cave, usually from a combination of bat guano, plants with root systems that enter into the cave (when the cave is close to the surface), and surface water flowing into the cave.
Most caves are quite 'dead' in the sense of having little or no life in them even when they aren't 'dead' in the sense that a speologist rather than a biologist will speak about a cave. You can go miles without seeing anything alive, even in a system like mammoth. On the other hand, some caves in Mexico that are very warm and have a large influx of organic material are so 'alive' that one of the major hazards of the cave is the sheer volume of living creatures in them. Seriously, the bugs alone can make it nearly impossible to breath without a filter. You also get caves were the amount of decay is so great, that they are carbon dioxide and/or methane rich and even if the bats are adapted to breathe it, you aren't.
But fine. I'm nothing like a cave expert. If Mammoth Cave wouldn't make a good dungeon, what cavern complex would?
A fantasy Mammoth Cave with more cave formations which is smaller and denser with things to do and see. Also, verticality is (IMO) awesome in a dungeon, and real caves have vertical terrain quite unlike almost anything that has ever been published. Indeed, you probably have to tone down the verticality and complexity in most real caves, which at least is comparatively small problem with Mammoth. But personally I'd rather have fewer interesting rooms rather than tons of almost identically shaped ones.
My advice would be to start with some of the smaller survey maps you can find online. I looked hard and found nothing on Mammoth that was particularly useful - just some sketches from 100 years ago showing a rather small part of the cave without much detail.
Has anyone turned any real-world cavern into a playable dungeon?
I'm sure plenty of people have, but I'm not sure you'll find good examples online. I usually piecemeal import rooms I've seen into a fantasy cave of my own design.
Still, I'm rather miffed that Mammoth survey maps aren't publically available. I understand why the caving community is so protective of its maps and even more protective of the location of entrances, but Mammoth is a freaking national park and world treasure. More to the point, it's not like Mammoth is a particularly delicate cave system with a lot of irreplaceable treasures of natural art that you must be protected from even a single inept intrusion. By this point, there ought to be explorable Minecraft maps of Mammoth.