I am currently migrating from Exchange 2010 to 2016 in a hybrid environment. We have public folders enabled in 2010 but there is no data in them and looks like no one has used them. I have quite a few questions dealing with public folders:
Do we have to migrate something that isn't used? - No; you don't actually have any thing to migrate.
How do we get rid of them if we do not need them? - Don't migrate the DB to 2016
As long as you are sure no one is utilizing Public Folders at all, then you should be fine not to migrate anything over.
In my opinion, shared mailboxes/resource mailboxes do the function of public folders without nearly as much as the administrative headache, and the client I'm migrating away from using public folders prefer not using them.