I know exactly what you mean (I think anyone who's done any crafting, gathering, desynthing, etc. is really familiar with the streaky RNG in this game). That doesn't necessarily mean that the algorithm itself is implemented or used incorrectly, but it does point out one of the problems I have with the game: namely, true randomness isn't very people-friendly, in my opinion.
People instinctively look for patterns in data, which causes number sequences with a lot of streakiness to appear less than random, even if they truly are randomly generated (e.g., sourced from radioisotope decay). Another problem is that the observable data sets we typically see in game as players are small enough that the effects of any streakiness are magnified. If you were able to meld a thousand materia, you probably would see something closely approximating the displayed success rate, but that doesn't make it feel any better when you're only melding 10 and they all fail (something that would happen about 6% of the time at a 25% individual success chance; considering how often you meld materia in the game, seeing something like this is almost guaranteed every now and then).
I would much rather see something like an asymptotically adjusted RNG, where every consecutive failure slightly increases your chance of success until you do succeed. Tuned properly, this could give results that wouldn't be truly random but would look much "nicer" from a person's perspective yet wouldn't deviate too much from true probabilities in the long term. Systems like this have been used in heavily-random games (see "smart RNG" in games like Destiny, mods for XCom, etc.), and from my own experience, they do feel better than truly random systems. The main problem with them is needing to track the current RNG weights for each action on a per-player basis, which in a game like FFXIV could be a pretty significant overhead.
So, TL;DR: server limitations (or developer philosophy, but it's fun to blame everything on server limitations).
I agree with this, in that I'd much rather have the rooms escalate in difficulty such that making it to deeper-in rooms would feel like a real accomplishment rather than just getting lucky. Maybe the Deep Dungeon coming in 3.35 will scratch that itch.


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