Only if you're constrained on connections. The reason that HTTP2 is much better for websites is because of the slow starts of TCP connections. If you're already connected, you don't suffer those losses, and you benefit from kernel muxing.
Here is a silly thing that is possible with h2 over a single connection, but not with websockets:
Multiple page components (Islands) each have their own stream of events over a single h2 connection. With websockets, you will need to roll your own multiplexing[1].
[1]: I think you can multiplex multiple websockets over a single h2 connection tho, but don't quote me on this.