Please let there be a Stream history setting
When you want to see a broadcast that already has been stopped, and you want to watch it again, the problem occurs when you can only view five broadcasts in the "Continue watching" tab. If you want to watch a broadcast that is older then the five most recent broadcast, you are out of luck.
And I don't think it would matter if it's already deleted, because chances are, it's still up. But if you really want to view an old broadcast that is still up, you gotta search and browse through thousands and thousands of broadcasts with a billion streamers uploading all the time.
If there was a "Continue Watching" setting, but if you click on the name, you'll see every broadcast you have seen, that would make the twitch experience a lot more enjoyable. You'll be able to see 20 or even 50 old broadcasts you've clicked on, and if it's still up, you'll find that stream you've been searching for.