I created https://omen.tv/ just last weekend. Similar in that it's powered by WebRTC, but it's designed for casting your screen (e.g. Jackbox Games) to other people's TVs.
My greatest annoyances with WebRTC were:
1. WebRTC requires a STUN server, and despite the spec initially supporting default ICE servers, it has since been pulled out into an extension because browser vendors don't want to provide servers[1]. There are free STUN servers (Google etc.) but...
2. Double NAT clients. STUN is inevitably going to discover double NAT clients. The only way to connect these clients is through a proxy. Specifically a TURN server. Unlike STUN servers, these are not light-weight, and I can totally understand why browser vendors don't offer them by default. So inevitably any WebRTC use still requires a self-hosted TURN server.
3. Inconsistent access to streams across browsers. In particular the getDisplayMedia[2] API provides poor availability of the audio stream. Courtesy of Apple doing Apple things, I don't believe it's even possible to implement this API on macOS as there's no audio loopback device. I worked around this for my use-case by installing BlackHole[3] (which is great software!) However, the loopback device appears as an input e.g. like a microphone, so isn't technically the display audio.
For this all to be smooth I think all these pain points need to be addressed.
Issue 1 and 2 require NAT to be kicked to the curb, come on IPv6! Issue 3, requires Apple to expose a loopback device and browsers to implement support. These aren't insurmountable issues, but they're unfortunately out of our hands as day-to-day devs.
[1] https://developer.mozilla.org/en-US/docs/Web/API/RTCPeerConn...
[2] https://developer.mozilla.org/en-US/docs/Web/API/MediaDevice...