Well I don't really agree that quantum computers are useful! Not yet anyway.
But in (most) distributed models of computing, networks of computers share bits back and forth. The quantum distributed models have computers sharing qubits. So this seems to be a practical implementation of a system that could solve certain problems (specifically some graph labelling problems) more efficiently (specifically, in fewer message-passing rounds).
Perhaps you're confusing "internet" (a network of computers) with "world wide web" (a set of linked documents)
I could see the usecase of a local network between quantum computers in the same room. The part where i get lost is why a wide area quantum network would be useful.
A priori, a quantum network could efficiently solve e.g. leadership election or shortest path type problems. I don't think there's any evidence that they can, but any problem you might want to solve for a wide area network is potentially a use case for quantum. By the way, as I said I'm more or less a QC skeptic in the sense that I don't think we will have scalable QC doing really useful work in our lifetimes. Happy to be wrong though.
As far as i am aware, none of the problems faster on a QC are helped in anyway by quantum internet.