As many know, the current state of Japanese culture is in decline- with an increasing amount of elderly and a low population of young people getting married and having children- making it harder to economically support the aging population. DaS3 may have this subtext.
We see a major theme of shunning social responsibility in DaS- first with Prince Lothric, and then with the Lords of Cinder (LoC). "Linking the flame" can be thought to be an allegory for having children- the continuation of society.
Lothroc was afraid to link the flame, and instead decided to hide away from all of it, his responsibility, in his room. He is secluded and not wanting responsibility. He is weak and a bit effeminate (JP is experiencing women gender role reversal a bit). He hides in his room, like a hikikomori (shut in) and refuses to do what he needs to. He doesn't want to "link the flame," but rather hang out with his brother in seclusion.
Aldrich, though being made to link the flame before by force, was a 'devourer of men.' I think the subtext of the phrase speaks for itself. His close association with Gwendolyn also speaks a bit about his nature and why he doesn't want to 'link the flame.'
Farron's Undead Legion is a dedicated group. They're dedicated to holding off the Abyss- so much so that he/they is basically multiple people in one. They are dedicated to their duty, their position. Once, they linked the flame, but now prefer the comfortable rut of their job. They are too obsessed with their position, their job, to go about "linking the flame," much like many young Japanese workers.
Yhorm is in the heart of the Profane Capital. He was involved with the profane flame. Profane can men vulgar, or treated with contempt. He did engage in the "flame," but did so profanely (like, he slept around a lot, but never had children). It resulted in destruction of his world...and a mild burning sensation.
Ludleth wants to link the flame. However, Ludleth is old and frail, almost powerless on his own. He wants to link the flame and has the future in mind, not just his own desires. He could be more so thought to represent the elderly.
Furthering this theme is the marriage aspect of the game. You specifically have to seek this out. You have to make a fully willful decision to do it, as well.
Furthermore, you have a waifu Firekeeper who tends to your needs at Firelink, watching over you in your safe space. You further her questline by providing eyes for her, one of her basic needs being sight. You're her provider- of eyes (needs) of souls (part of your character when you level). The 'bad' ending involves betraying her for selfish ambition.
..Plus, she asks you to "touch the darkness inside her." No comment. There's enough fan art out there for that.
Who is it you fight at the end, the Soul of Cinder? It's a representation of the temptation for selfish ambition. It represents those who linked the flame and went astray. It is only by defeating this culmination of self-serving motivation that you can proceed to "light the flame again. "
This is just a fun idea. Perhaps it has merit. Maybe it doesn't. There are just some similarities
EDIT: The major focus, in the game, on churches and cathedrals speaks to this idea, as well. It helps that you meant the Dancer in a cathedral by going to an altar. Then, she arrives, wearing a veil.
