A suggestion, not a better one. Narratively Dark Souls 2 is actually the best of three, even if you don't lore-master it (although since in Scholar you can't unlock the Shrine of Winter without having acquired the Great Souls, which changes the dynamic of the narrative a bit; in vanilla the Shrine would open to you without the Great Souls if you had acquired a huge number of regular souls):
Besides the main quest Dark Souls and especially Dark Souls 3 are very much a compilation of stories that touch the main quest but aren't really connected to it.
In Dark Souls you have the carriers of the Lord Souls, which have widely different motives regarding the First Flame:
- Gwyn preserved the First Flame by the becoming the first Lord of Cinder,
- The Witch of Izalith drowned her kingdom in an attempt to recreate the First Flame in order to prevent the loss waning of the First Flame from ending the First Age of Fire,
- Seath the Scaleless is indifferent to the First Flame now that he has finally found a way to achieve the immortality he was denied by being born without the scales of an Eternal Dragon,
- the Kings of New Londor sold themselves to the Abyss for the power of the Darkwraiths after the part of Gwyn's Lord Souls they were given failed to satiate their ambitions for power and dominion.
- Nito is content to watch the world decay because he an avatar of death and decay himself,
Either ending of Dark Souls however renders any of these ambitions meaningless as you either become the Second Lord of Cinder or the Dark Lord, both of which play into inevitibilty of the world decaying and dying since the First Flame introduced Disparity into the world. As the state of the world boils down to side effect of the First Flame fading, you can't even say they are responsible for the state of the world.
In Dark Souls 3 you have the Five Final Lords of Cinder whose ashes you have to collect in order to access the First Flame, each of them has turned away from their fated duty as Lord of Cinder due to an overriding obsession:
- The Young Prince Lothric would not leave the side of his undead brother who had protected the sickly younger sibling while their father's obsession with the Eternal Dragons turned him away from taking care of the kingdom.
- The Abyss Watchers were obsessed with destroying the presence of the Abyss in any shape or form, however being humans they too are creatures of the Dark and therefor akin to the Abyss; this caused them to fall on each other despite the pact through the Blood of the Wolf.
- Yhorm the Giant was obsessed with destroying the Profaned Flame, a strange imitation of the First Flame that would not fade but also not give life.
- Aldrich was driven mad by visions of a flooded world and sought to survive in that future only he could see by casting off everything he was and devouring anything to promised to make him stronger once he took it into himself.
- Ludleth of Courland (who is already in Firelink Shrine) has also a strong desire to prevent the World Without Fire.
Again, both their duty and obsession are rendered pointless by the endings, regardless if you fulfil, betray or usurp your duty as the Ashen One - the world will decay eventually (as linking the fire doesn't stop the First Flame from fading anyway) or through your actions (either by letting the First Flame fade and the world return into a darkness without Disparity or whatever will happened once you take up the mantle of the Lord of Hollows). Unlike Dark Souls, there is however a case that can be made that the call for an Ashen One as a measure of last resort can be blamed on four of these five (Ludleth at least came willingly).
Now this idea of strong, destructive obsession is also present in the Bearers of the Great Souls in Dark Souls 2, especially at Bonefire Intensity 2+ when the Great Souls come with names that reference Dark Souls; although there seems to be an inversion of the original theme at play here. However this only exist a thematic through line for the series and is only tangentially related the story that is told through the locations across the critical path of Dark Souls 2 - many of the optional locations don't tie into this (don't ask me what the Executioner's Chariot is about
The ciritical path tells are more in-depth and coherent story: the tragedy of King Vendrick, the man who could not be link the fire, the king who could not be a Lord.
From the Forest of the Fallen Giants (representing the both the rise and downfall of Drangleigh as a kingdom) to the confrontation at the Throne of Want, the story is one of ambition to conquer both a kingdom and the fated curse of that would come with the fading of the fire*:
*A big fan-theory here: During the events of Dark Souls 2 the threat to the First Flame is not that it has faded as far as in Dark Souls but the presence of Nashandra, which as daughter of the Abyss might snuff out the flame; this is what is calling your Undead to Drangleigh not the immediate need for a new Lord of Cinder.
Vendrick and Aldia tried to prevent the Undead Curse by many means, including trying to recreate an Eternal Dragon and creation of the Emerald Herald. Like al l candidates to be Lords of Cinder of their age they attracted a daughter of the Abyss, Nashandra. Vendrick fell in love with Nashandra and with her help he found the location of the Throne of Want and build a castle there.
Eventually despite his love for her Vendric was able to detect Nashandra's true nature; and faced the crushing truth that he could not claim the Throne of Want (and with it the possible solution to the Curse), Vendrick chose to sequester himself in the Undead Crypt. His isolation guaranteed by his knights, he turned into a mindless Hollow.
Thanks to the more linear approach to how you progress (checking off one location to gain access to another, thank you Fragrant Branch of Yore), the story unfolds naturally - even though you have to do some exploring and reading of item descriptions for that (and you may also miss informative encounters, like returning to the Undead Crypt with the Ashen Mist Heart). On top of that if you put all the pieces together, the story has tangible stakes and plays into theme of an inevitable fall without denying the agency of the characters involved (e.g. Vendrick becomes a Hollow because he choses to, not because he was always going to be) - which is helped by the ambiguous nature of the ending (or both endings, if you are playing Scholar).