We do not compile Cobol programs in production, so I do not think there would be an issue with not doing it.
We do compile maps and dialogs, I think in order to ensure that all components are moved, but we do not use the resulting load modules, opting to use the modules that were tested in our QA environment.
I worked in one organization where all programs were compiled when moved to production based on the new production source. I believe the reason was they wanted to make sure that the production source was up to date. It allowed us to confidently recompile large batches of programs without worrying about the state of the source.