The user would do it to grant your app the functionality it needs to actually do what you want it to do.
OAuth is an industry standard, there are many examples and guides on how to implement it, it is not a complex system and is how many bots and services on Twitch operate and handle thousands of end users without issue.
It’s really not a massive amount of data. If you use User tokens then even if a streamer wants to look up 1,000 channels, that’s only 10 requests per minute per user. Even if for some reason a Discord server wanted announcements for 80,000 streamers, that’s still 800 requests per minute and perfectly fine with the rate limit.
You do not know how this scales internally at Twitch. The simple fact there are are rate limits that prevent you doing what you intend to do with EventSub, but do allow you to do without issue with User Tokens and polling the API is perhaps indicative that polling the API is the ideal option for your use case. It may not be ideal for you, but for Twitch it may be.
Again, this is solved by using User tokens. 800 requests for each and every user of your bot should be more than sufficient to get all the channels they need once per minute. If your app caches results then where multiple users are interested in the status of the same streamer this can further reduce the number of requests needing to be made.
The options to do what you’re doing at scale are already there, user tokens. It’s how most other apps scale, include those that make millions of requests on behalf of thousands of their users.