I think the best way to describe Wall Drug is that it's an experience. Love it or loathe it, it's completely unique. From the free water to the godawful animatronics. And you've got a point about Mt. Rushmore. One of the more interesting things to me is how much they love Custer out there. For a lot of people, he's just known for the last stand bearing his name, and is seen as a dumbass at best. In South Dakota he's basically a folk hero.
I have never been to Wall Drug but I have been to South of the Border when I was a kid. I remember all the signs to see South of the Border all throughout the highway. For some odd reason, I remember them having really good pizza. But maybe it was my kid tastebuds that thought that way. I do also think I played mini golf there as well. It was probably the best tourist trap I ever went to.
Never been to SotB but I have seen some signs for it in passing. Definitely a Wall Drug kind of vibe. Another one of my favorites is Santa's Land Office.