You say you don't want to know the technical know-how's and whatnot, but that's a very large part of the issue itself, it doesn't matter how much actual interest there is if trying to achieve what they want to achieve with the private server is technically infeasible. There are a small number of private servers out there, but they are privately owned by one or a small number of individuals entirely for the purposes of datamining aesthetic stuff in-game before the latest patch goes live, as said servers have zero combat / enemy AI functionality.

The biggest issue with trying to make a private server akin to WoW or other games is the fact that unlike plenty of other games where boss scripts are saved with the client thus massively expediting the process, FF14 entirely saves its enemy AI scripts server side (as well as most NPC scripts). Meaning to create a private server for FF14 that effectively isn't just 'walk around and enjoy the scenery', you'd effectively have to re-program the entire game, every encounter, every NPC, every mob by hand; a monumental task for what is ultimately a small payoff with insanely high risk.

Because lets be realistic, as much as people love to chalk up Heavensward / Stormblood, those expansions are lacking so much QoL the game experiences nowadays that very few would actually want to go back and play it in any long-term capacity, just for a short bit to go re-live combat nostalgia, so any private server would have to do all that work for ARR + two expansions for the majority to even have the slightest interest, because ARR by itself isn't gonna be turning any heads on its own. But then what is even the point of all the work when a single cease & desist letter from Square would render months, if not years of hard work manually reconstructing the game nullified in an instant?

As for your example of a private server of RP - why would you bother making a private server that would be played by such a minuscule amount of the playerbase for RP when the live game already has many RP-thriving worlds filled with thousands, if not tens of thousands of potential RP partners?