For me, I always understood it as he had completed everything he needed to do in that life... and so at last, he is able to rest. In peace, without fear nor worry.
Cosette has found a man who he knows will love &and protect her, taking from him that responsibility, one that he volunteered for of course (one that he changed his life for &and that gave him purpose) & there. There certainly is a moral dilemma, when after he receives news from Gavroche (Fun Factfun fact: Eponine's brother) about the men at the blockade, prepared to diedie; including Marius who, as he reads the message he's received (addressed to Cosette), makes him realize that Cosette & MariiusMarius are indeed in love. The decision he sings about having to make is to either let him die or to save him, singing that the existence of this love of Cosette's is something he's always dreaded. Dreaded? What? Being replaced? Losing Cosette? The loss of Cosette's youth? Considering the unwanted possibility that she will need him no more? That it is Cosette's time? She, Marius & the family they will have. The thought of ValJean eventually becoming a burden to Cosette, when she has to care for him as an elderly man?
The feud with Javert has ended.
He is sick of running. He is sick of hiding. There's that strong line when he sings "My name is Jean ValJeanValjean. 24601" as he takes back his true identity. What would be left for Valjean? Everyone he cares about is safe or dead, he is still wanted by the police for desertion, although I don't think that plays into the decision. He is certainly not scared of anyone &and is using his true name. I just believe he is tired, his work in this life is done so he feels safe to enter his eternal sleep (&and he deserves it).
PS. I've seen multiple stage productions of Les Mis. Have 1 of the live versions on cassette but no one beats Hugh Jackman! And certainly not Russell Crowe!