What solution do you think there can be for a stream with thousands of people watching?

They can definitely improve upon it by message-limiting and message-length limiting (maybe they already do that? I always disable the chat)

Really, the people who care about the chat I imagine are under 20 and hence take internet communication with strangers seriously. I had great fun in my day being a total dipshit online while playing computer games, it was part of the fun for me.

What they can do is have multiple chats, some free-for-all, some moderated, etc. Except, I don't know who's running Twitch but they could've done a thousand and one things to improve their platform and I haven't seen anything, so. It is what it is :)

It's frankly plenty good enough for me. I've written an app for iOS that lets me know when more than X number of people are watching a game (GameWhen on iOS App Store) I'm interested in so I don't miss the big tournaments, outside of that, the streams don't lag, the tournaments are bigger than ever, life's good :)