My issue isn't with the level of technology, or the details of what's happening. As you say, we already have highly-advanced robots/AI and crossing dimensions and timelines (though in a way that adding more makes it messy).
My issue with it is that these specific highly-advanced robots and this specific story already have their own game and universe to exist in, and that universe should not be integrated into this one.
If they want to tell further parts of the NieR story, make another NieR game instead of forcing it into another game entirely.
I dislike the prospect that if the two games are canonically merged, suddenly all of NieR/Drakengard is part of the same series as FFXIV and becomes "required reading" to fully understand what's going on. It already seems to be the case for understanding this raid. It's why I really hope that this crossover will not have further reach beyond this specific storyline.
Ivalice had a lot of the same issues - heavy reliance on another game's plot, and a seeming expectation that you'd like the characters because they were from that game, without trying to make them interesting in their own right. But at least that was another Final Fantasy game.
(If their aim is to encourage FFXIV fans to go play the other games, it's not working for me. Maybe I'm just being stubborn and digging my heels in, but I'm not going to go and play a game I wasn't interested in just so I can understand this one.)
This major crossover with an unrelated game also sets a precedent that I don't want to see followed. Previously, with the exception of minor events, the story was either original or based on Final Fantasy series titles. Now it crosses over with an unrelated game in a way that gives it a huge level of billing - higher even than several actual FF crossovers that were treated as temporary, inconsequential events. (The FFXV event could have dropped some lore bombs about crossing dimensions and shards, and the nature of primals via not-Garuda, but we all glanced at it and said "yeah whatever, it's just a crossover, they're not canon".)
Either this opens the floodgates of more major crossovers with other games until FFXIV becomes a weird mess of other stories making it harder to tell its own, or NieR forever sits alone as the one non-FF game that was somehow special enough to get an entire permanent raid series dedicated to it.
It also, as I said earlier, makes alternate dimensions messier.
The FFXIV structure as established in the main game has one universe with a possibly-localised splitting into shards. To that we add an apparent split-or-overwritten timeline for the universe.
If we now have to add "alternate universes" that's another layer of complication.