It does something, if the fanservice is appealing in a way that makes people who don't have nostalgia go look up the source. Some people even find a new favorite entry to the series or a new favorite game.
Also I'd argue that Yorha can't be nostalgic, as it's not really old enough to give anybody nostalgia.
As far as Omega goes, the source of the fights are explained as being from data within Omega, both fictional and not. As for why those bosses, well, if they'd left the final forms in the normal mode instead of just relegating them to Savage it'd be more apparent. Each tier follows the pattern of Monster that controls positioning > Monster with gimmick powers > Strong Monster with both of those > A literal planet destroying God. As with a lot of Stormblood they hoped to tell part of the story within the gameplay, and yes, they failed at this attempt, mostly. It's mainly because Alphascape has to buck the trend and goes God of Elements > Father of Dragons > Omega > Omega. Of course, it also all serves to get us amped up and believe Omega is wildly more powerful than all of these things, since it can emulate their powers in holodeck simulations.
As for why Ultros appears in Sigmascape 3.0, it is because The Guardian in FFVI uses the attack patterns of all prior bosses in that game, and they decided to select him as one of the boss patterns to emulate in XIV, since they already had his model and mechanics made up from other trials. They also made it emulate an FFXIV boss, The Everliving Bibliotaph so, there's that. As far as a lore reason, I don't think one was given. But I mean, his initial appearance in FFXIV is pretty much on the same level, "Oh he's some sorta voidsent accidentally summoned here." So he's just there in XIV, too, with no real backstory extrapolated on, because Ultros is nostalgic fanservice content in the first place.