We've always had 'compile once, run anywhere' but there's always been caveats and gotchas.
I don’t think it will replace Docker files since they let you package up such a wide variety of existing server software and WASM is more limited. But if your software does compile to WASM then maybe you don’t care about that.
I think of WASM more like a plugin format, but I expect there will be a lot of engineering effort put into optimizing it, like happened with V8 for JavaScript. Not all web standards win, but betting against one that’s well-established and has a lot of support seems like a mistake.
For the stuff people run on their Kubernetes clusters I have more mixed expectations. Containers are more universal, but I can totally see a microservice architecture running as a lot of WASM runtimes with a handful of containers.