I don't think a Snow White Mine Car ride would be that much more popular than the ride that's already there. We have Casey Jr. which goes around, but the fun of that is being a circus animal with a train that has a personality of wanting to make it over the hill. What would you see in the Mine Car ride? Just dwarves working and a whole lot of gems. Right? Does Snow White ever go into the mine? Would you see the animals, the witch, the scary woods... anything?
You say people like Spash Mountain because it has an unknown story of Song of the South. Not true. It's popular because CA is hot and it's a water flume ride with a nice thrilling drop first and foremost. The characters and story within are what makes the ride memorable. And you don't have to know the story, or you can know it like the back of your hand... it's still plain good fun. The ride is called Splash Mountain, not Song of the South: The Ride.
It doesn't matter if the ride is inspired by something, completely original, or a recreation of a film. If it's done well, people will enjoy it and ride it again and again. Disneyland is great for its variety of entertainment and the recreation of a film is what makes Fantasyland so special. Is there room for improvement in those dark rides? Definitely. But to tear it out for attractions that have no recognizable characters? Not a chance. Disney was the one that ultimately made up his mind of how Fantasyland was to be. If he was really unhappy with it, it would have changed while he was still alive.