(1) distributed computation. If you can network two quantum computers, you essentially have one quantum computer with twice the storage. Quantum networks avoid the need to build one enormous quantum computer.

(2) easier experiments. Currently, doing a loophole free Bell inequality test is hard enough that people get PhDs for it. With a quantum network that experiment is way easier, because the network solves the hard part (distributing the entanglement). You could probably also use quantum networks for other experimental tasks, like coherently linking telescopes on separate continents, though the bandwidth and computational requirements for that would probably be a bit insane.

There are also some more out there ideas, like if stock markets contain Bell inequalities then you could use a quantum network to build up entanglement that is then consumed to win those games more often which equals $$$. But it's hard to imagine concrete scenarios that would create such an inequality, nevermind one where the expected dollars gained from the quantum strategy exceeded the cost of operating the network.