I’m not sure I’d call his use case “unique”. Speedrunslive.com’s homepage is a very similar case. It gives you a list of live speedrun streams and embeds one of the higher-viewer streams at the top by default to try to get you to check out a new speedrunner. It also embeds chat, and if you hover over the stream you can follow, subscribe, or click the title to be taken to Twitch and check out their channel description or VODs or whatever. In my eyes, I’m already getting the “full [streamer name] experience” that your popup describes, and the popup only serves to damage the experience I get by watching on SRL.
The embedded stream on SRL isn’t the focus of the web site, just a bonus, so it’s easy to just skip past the featured stream and go find a race to join if the stream doesn’t auto-play uninterrupted. The streamer’s only got a few seconds to catch my interest before I move on, and you’re making it harder with this feature.