Same here. The only way to make streaming between devices is the way Apple does it, directly, not via Access Point.

Mirecast (when done properly) is basically a video stream over a peer-to-peer WiFi Direct connection. H.264+AAC/AC3/PCM audio sent over RTSP/RTP using a standard IPv4 stack. Better codecs are available on newer devices. Two modern WiFi 6 devices can stream gigabits per second that way if configured right, there's no need for the typical low FPS, lag, and desynchronised audio from a protocol standpoint.

For some reason, a lot of implementations (especially on the receiving end) suck at this. The latency seems to be terrible and TVs and displays seem to care more about reassembling old frames than about showing the latest good signal. However, it's not all that different from what Apple is doing.

Miracast over ethernet/via an access point is something different (something I've never really seen used myself).

Doesn't Apple do it by having the AirPlay receiver be its own access point? LAN in comparison indeed isn't ideal.