The point of A Christmas Carol isn't the salvation of Scrooge's soul. That's secondary. Frankly, we don't know what happens to Scrooge's soul. It might be that the chains you forge in life remain with you always.
The point is that Tiny Tim doesn't die.
That, in microcosm, is the difference between the religion practiced by many people and truly living a good life. You'll notice that Dickens doesn't send Jesus to Scrooge to tell him he's being a bad man. There's not much about Christianity in A Christmas Carol, really. The Spirits aren't angels. And they don't show Scrooge that his place should be giving his money to the church and praying for salvation.
A Christmas Carol is a worldly tale of what might happen to Scrooge in this life, not the next. His salvation, if it can be called that, is found not in faith but in action. We're never treated to a homily on the true meaning of Christmas being a baby in a manger. We see Christmases Past, Present, and Future as people observe them. The future for Scrooge may be bleak, but it is still Christmas. In fact, one could make the point that only by showing Scrooge the real-world consequences of his actions can his actions be changed. If he needed to hear about the Hell that awaits the rich man, Marley told him that at the outset.
But why save Scrooge? A wretched old miser if ever there was one. Sure, the story is directed at people who are in similar need of salvation, but the end of the story doesn't make it clear that Scrooge achieves salvation. He just doesn't die hated and alone.
No, the Spirits change Scrooge not for himself but to save Tiny Tim, and by extension the Cratchits as a family. And then, by further extension, all the other poor people who will be saved by Scrooge's change of heart. But Tiny Tim is the start. To save even one life is blessed.
So when people ask why the Spirits put so much effort into changing Scrooge, who doesn't deserve it, remember how the story ends. Tiny Tim doesn't die. Dickens wants you to know that in no uncertain terms. He stresses it. Tiny Tim, who did NOT die.
The lesson you should take from A Christmas Carol is to keep your Tiny Tim alive however possible and worry about theology later.