Define license when publishing files, and display it in song page
What is the problem you are facing?
License information should be visible in the pages of the songs published. If this information doesn't come as metadata in the files uploaded (as far as I can see MusicBrainz doesn't include it), the uploading process should provide a way to define it.
Currently Funkwhale says when uploading a file:
You are not uploading copyrighted content in a public library, otherwise you may be infringing the law
While this is true, uploading content with free licenses often requires some legal compliance too, and more importantly to respect the terms of the license defined by the owners of the creative works. For instance, the license Creative Commons Attribution Share Alike requires to "provide a link to the license".
What are the possible drawbacks or issues with the requested changes?
Implementing this feature requires development work, but legal compliance is intrinsic work in a software project.
Implementing this feature adds a step for users uploading files, and many users may not know the information and be annoyed by this step. This could be relaxed by having a configuration for administrators that would allow to disable it in private installations or "at your own risk". All in all, users having a clue about the licenses of the content they upload cannot be a bad thing.
There is the risk of users introducing wrong license information in good or bad faith, and then someone should be able to correct that information.
If you go ahead with this feature, you may want to emulate the file uploading process in https://commons.wikimedia.org, where they have figured out all this with a professional legal team behind. For what is worth, the information and source code can be found at https://www.mediawiki.org/wiki/Extension:UploadWizard