Even if they tried I don’t think they have the leverage to make that work. What games or publishers are big enough that such a move would go worse for Twitch than it would for them? Most of the time indie games make for better content anyway. Twitch could just ban games that don’t include an unconditional free streaming license in their terms of service and not lose much of any popularity, while the game publishers trying to extort them would absolutely lose popularity.
Even if they tried I don’t think they have the leverage to make that work. What games or publishers are big enough that such a move would go worse for Twitch than it would for them? Most of the time indie games make for better content anyway. Twitch could just ban games that don’t include an unconditional free streaming license in their terms of service and not lose much of any popularity, while the game publishers trying to extort them would absolutely lose popularity.