Are My Bookshelf Plans a Bad Idea?

I'm thinking of building some solid wood bookshelves with a really minimalist design—basically just a back and shelves, no sides. I know this might not be the best idea, but here's what I'm planning: the back will be a 1" thick solid hardwood and will be screwed into the stud for support. The shelves will also be hardwood and likely an inch thick. I'm using a through dado joint with horizontal wedges on both sides of the shelves. My main concerns are whether this joint will be strong enough to support a standard bookshelf load and if it's a bad idea to put that much weight on the stud. I'd appreciate any suggestions or insights! Thanks!