Every user of your plugin wouldn’t have to request a limit increase, unless you’re expecting each user to also go through the process of registering an app on Twitch and inputting their client id into your app for it to use.
Also, are you not performing any form of caching? If you take just Monstercat from your example, is your app really making every single end user send a request to Twitch to get Monstercat’s follower count? That’s very inefficient when you could just have a server make a single request, cache the result, and the end users get the data from that cache rather than make redundant calls to Twitch’s API. If you multiply that by the number of duplicate streamers that the end users may be requesting data for and that is quite excessive without caching.