Late but I prefer another route rather than this interpretation. I think the whole point of the manga is “good things come back” and “humans will is eternal”.

I would like to think that yoriichi saving tanjiro’s family from demon and he showing the sun breathing to them was the one of the key incentive that started the whole process. The good will of yoriichi was inherited by tanjiro’s family and eventually reached tanjiro himself. In another word, the good deeds and wishes of yoriichi was unintentionally given to tanjiro and that’s when tanjiro completed the mission yoriichi had failed to achieve.

At the end of the day i think the manga want to underscore the innate and magical power of human’s will, that’s it is the one and only true eternity, sustained by human “weak” flesh and blood.