I mean, aside from saving their lives, I’d argue that the direwolves are also emotionally hugely important as well. Jon loves and trusts Ghost a great deal; he’s cried with Ghost, confided in him, worried about him, and it’s through Ghost that Jon is able to get a measure of how his siblings are doing. He’s comforted by the presence of Ghost’s litter-mates in his wolf dreams, because they’re a direct line to his own siblings. This same contact is seen with Arya and Bran, and it’s what grounds Arya and reminds her that she’s a Stark with siblings she can one day reunite with. Conversely, it’s part of Sansa’s isolation, because she doesn’t know that Bran, Rickon, and Arya are alive, and doesn’t have a wolf to comfort her. When you remove the direwolves from the story, you leave behind a family that loses a crucial bond and their emotional support animals. The direwolves are part of the family, and that matters for a family that’s always been very close.
Compared to Daenerys, who has no family, instead created a chosen family, among them her own “children”: dragons. They are more than just weapons to her. Well before they could even be considered weapons, they were entirely reliant on her for food and care. She raised them from hatchlings to ferocious beasts, but in the process loses control of them, which is very much analogous to a parent’s experience of their children growing up and no longer needing them.
Moreover, the dragons are the causes of her problems as often as they are the solution to them. Things don’t go easy breezy beautiful because Daenerys has dragons; they’re a novelty that the greedy around her are dying to get their hands on, either through trickery or marriage or murder. Dragons are selfish, self-sufficient creatures who don’t know the difference between human and animal, and don’t care. And that’s where the dragons are meaningless if Daenerys wasn’t their mistress: they don’t care.
Dragons don’t care about slavery, or rapes, or children, or women, or thrones, or power. They don’t make policy decisions, they don’t strategize, they don’t plan battles. They can’t make emotional pleas, they aren’t charismatic, they can’t negotiate. Let them roam free and they’ll eat whatever and whoever they want, they’ll destroy cities if they feel like it, and they won’t care one whit for the social structures that humans created. Without Daenerys, the dragons are nothing but fearsome killers. With Daenerys, they can be put to a purpose, and the consequences of that purpose would rest solely on her.