Don’t assume that using a first party client-id will last forever either. Twitch are obviously scaling back access and removing some of these endpoints which were never intended for third party use. Even using the workaround you’re suggesting can and will break in the future.
Perhaps take the hint that Twitch doesn’t want you using these API’s and invest your dev time into something to use instead for when these endpoints eventually become fully inaccessible to you. And if there’s not a suitable endpoint currently then suggest it https://twitch.uservoice.com/forums/310213-developers as that’s where Twitch look for how much demand there is for new features and if there’s a justifiable use case.