I don't know about LiveKit, but I work at Daily (https://www.daily.co) which uses WebRTC for client connections.

You can definitely use Daily to build a Twitch clone and beyond — we have a powerful API for custom layouts and graphics in live streams.

You certainly could, there are some folks in the community building Twitch-like livestreaming experiences with LiveKit. One of my teammates built a mobile livestreaming demo app, perhaps I can convince him to release the code. ;)

Update: Given that this is for internal use at your company, a single LiveKit node should be perfectly fit to handle the scale you need.

Do you want to build a Twitch clone, or are you unhappy for one reason or another with the existing selfhostable FOSS projects doing this?

You can do it with WebRTC just remember that it is meant for low latency video connections. The trade off is a higher bitrate and no caching.