What you mean here is actually deps pinning + vendoring. It's way out of scope of basic CI concept.

CI doesn't help when all the dependencies aren't locked, or where some deps disappear, or ...

Not for running the project locally

I think you're missing the point.

CI solves it because it proves that it can build in the pipeline, using a well defined environment.

No guessing at which node version you need or any other dependencies that may be required.