In a recent committee meeting with fellow publishers, I was accused of not being a "proper" publisher. The accuser said this in response to my comment that I was not particularly interested in "securing Swedish covers of our songs", but far more interested in making sure to get paid for airplay on Swedish radio and mechanicals from online services in Sweden. (This exchange was in a discussion specifically about Sweden, but applies equally to other territories).
It highlights how not all publishers are the same.
The publisher who made the offensive remark, is a very traditional publisher. He works with songwriters who provide him with songs, which he then pitches to artists and labels to get recorded and released. That is a perfectly valid business model, but not the one and only "proper" publishing model.
I work with artists who write their own music, most of whom are DJ/Producers. Publishing is one of a number of services that I offer them through my company Musiqware. Those services are not about securing cover recordings, but much more about securing payment for all uses of their music, wherever in the world such uses occur. We make sure that their music is registered with numerous collecting societies (and various other organisations that license direct), and that those registrations contain as much as possible additional data to assist with identifying all uses of the tracks. It also involves sending all music to music recognition technology companies to ensure that uses are reported. We also pitch and license music to film, TV shows, commercials, corporate presentations, online videos, and so on, either direct or through third party agencies.
But we do not look for covers, because that is mostly irrelevant to the artists we work with.
Not all publishers offer the same services, nor do they all have the same priorities. There is more than one "proper" publishing model.