I do not have a real cheese cave. I have a modified refrigerator.
If the point of a real cave is the relatively free cost of maintaining evironmental control, I guess I would have to ask what the return on investment would be compared to using comercial (and artificial) environmental controls.
So, a natural cave might cost little over time, but might be a huge cost up front, while commercial "reefer" might cost a lot less initially, but have ongoing costs over time.
A natural cave might also be a bit more dificult to "fine tune" when it comes to temp/humidity.
So, if your return on investment is relatively short, and you find that you get the kind of environmental controls you need from a natural cave, then I would say go for it. It certainly sounds cool.
But If I did, here are the things that I would want.
Lights, small fan (i would run electricity)