Why doesn't Twitch have their own donation system so they can take a cut of donations? Basically they need to implement StreamTip. They can then forbid partners (streamers who are allowed to have subs) from having any 3rd party tipping services. It's bad for StreamTip, but the profits for Twitch would be HUGE. There are some streamers, such as Lirik, whose main income from Twitch is probably tips. StreamTip already takes a cut of the tip, so it's not like the streamer would lose money if Twitch had their own tipping service.
This is how a lot of Chinese and Korean streaming services operate. And integrated donation system can allow for more interactive options between streamer and audiences, or even between audiences. (Like streamer present the audiences with two options, and the option that getting more donations will be chosen by the streamer.)