We can do this now, but I don't think the user experience makes it worth it compared to casting. Bandwidth limitations require lower frame rates and responsiveness, which is fine for video but bad for interactive apps (most phones are native 120+hz + VRR_. But re-encoding video is (processor & battery life) expensive and probably lower quality than the original stream.

People who do this a lot probably just use a DV adapter (maybe it just works with USB-C, but I haven't tried it) for native apps, or casting for streaming video.