A toy project, but I'm working on a Scrabble clone for my mother to play. There's singleplayer against an AI, and then multiplayer against other people (myself, mostly). Multiplayer needs a server backend with all the game logic which I have programmed in Rust, but there's no reason I can't have the game logic for singleplayer running entirely in the browser.
By compiling my backend code to WASM I basically do that - the client can use either a client-side 'server' or connect to a real server. The UI code itself is unchanged in either case.
I suppose the need in this case is that I have code written in a language other than JS and I want to run it in a browser; inversely I could have written the entire project in JS and hosted my backend server on say Node.