Most of these apply to every Warden, and the few don't, don't apply to every HoF so can't be used.
Cure for the taint - relevant to every Warden.
Business as Weisshaupt - could be any warden
Solas - literally applies to every single person in the world
Feraldan - equally likely to be Anora here, guess Anora should be the new main character
Morrigan/kiaran - sure, relevant Warden can come back to deal with those if something major happens with then, but it probably won't as Kiaran doesn't even exist in a lot of world's.
Leiliana - doubt she's going to play a role. If I'm wrong, sure, the few Wardens that this is relevant for can come back for that quest.
Warden Commander - plenty of important people in the Wardens that could take this place a lot easier. Nothing that needs to involve the HoF. We won't be anywhere near Feraldan in the first place, we're going Tevinter.
Elf - so every elf character needs to come back simply because they are an Elf? Not to mention, only applies to about 10% of wardens
Fade - what exactly do they know here?
So, sure, I guess they can come for the sidequest with Morrigan if they romanced her, but that's a very small minority of Wardens that need to return.
Nope, if it applies to ANY Hero, then it is relevant and is a reason for EVERY Hero's return. In other words, if even one Hero has one reason to return, then all of them must return.
And the Hero has the cure, so the Hero's return is assured.
What's going down at Weisshaupt is too much for most Wardens. The order needs the Warden-Commander.
But not just anyone will be able to stand against Solas. The (ex)Inquisitor will need the Hero, possibly even the Hero King of Ferelden to help stop Solas' plans.
Anora needs help after all that happened, and the Hero is one of Ferelden's monarchs. He will return for that if nothing else.
But they do exist as a family in some worldstates, therefore all Heroes must return.
The Hero who romanced her already returns and spends time with her. So that's that man. The Hero returns! And if the Hero returns for that, why not apply it to more than just that one thing?
But the Warden-Commander will be needed at Weisshaupt to deal with whatever problems they are facing, and Weisshaupt is near Tevinter. Hawke or Alistogain are there too.
Yes. Every elven Hero is relevant to the story because Solas is calling all elves. That makes the elven Hero a valuable person in the (ex)Inquisitor's plan to gather people who can help stop Solas.
The Hero has been to the Fade at least twice, possibly up to four times! The Hero is well experienced in navigating the Fade and dealing with spirits of all kinds. I will also add that many Heroes have already defeated one of the Forbidden Ones.
I would also add Alistair to this. He could survive Adamant and go to Weisshaupt. A female Hero who romanced him will likely meet up with him there upon returning to southern Thedas.
So clearly the Hero of Ferelden is incredibly relevant to the plots of the series.
So This Problem Exists:
If they were to try to reimpliment the Warden in later games for those who performed the Rit, or had it performed, they would need to impliment an entire character, voice actor, retroactive (as with Hawke) face modeling process, bit of the story line, etc..., and couldn't do anything major plot-wise with said Warden due to it clashing to much with what would be the canonical plot, in which he/she would have never, ever been involved due to dying.
This problem was solved in Awakening, the expansion to Origins. The Orlesian Warden-Commander has all the same race/sex/class options and all the same voice selections as the Hero. The Orlesian Warden always survives. This character can fill in for the dead Heroes.