The proof was in the counter example I provided, which is one of many. There are clearly instances where labor is present, but there isn't any value being generated. If labor had intrinsic value, that would not be the case.

I'm not discounting the value of labor relative to output, and it's clearly related to how we assign value to that output, but I think the labor theory of value is too simplistic and places too much value on labor and not enough value on utility.