Probably not, as self-hosters are disproportionately affected by spurious or malicious copyright claims (they don't have the pooled resources to fight).
On the other hand, the copyright owners will have a harder time finding the allegedly infringing material. A bot that can find and scrape media on any website needs to be pretty advanced, especially if the site is using encrypted media extensions. And after that, getting into contact with the owner of the site is not trivial. It won't be worth the effort in the majority of cases. The centralisation of media on youtube, soundcloud etc has been very practical for litigious copyright owners.
Those services do not necessarily need to be publicly accessible. Think of a federated network of private servers with closed user groups, which allow to share stuff easily with selected users on other servers. The directive would probably not even apply to this, but even if it does, it would be pretty hard to go after you, ay long as you don't share critical material with people you don't know.
That's precisely why there are societies of authors, editors, publishers, etc. => in part in order to protect from malicious claims.