I don't expect anyone to "control it" by themselves, the internet can be a cesspool at times. Imo twitch does need to lay down some clear guidelines, but as a streamer some of the responsibility has to be on you. Don't give out anything you don't need too, sure mistakes will happen just don't do it willingly unless you are prepared for the results steaming from it.
Let's have a look at another issue Streamers and YouTubers face, "get togethers", if you just dropped into a coffee shop and told the Internet "hey I'm at XYZ, come and have a coffee with me" then people will come expecting to have a coffee with you. But unless you have sought permission from the person running that coffee shop you are really going to piss them off, they won't be expecting an high number of customers, they will be understaffed and customers including there regulars will have a negative experience of your coffee shop. The stream may think "what's the problem? I didn't nothing wrong, that guy should be grateful for the extra business I brought him...". And that's if no one is being a dick. The Greater Internet Fuckwad Theory means that given the anonymity provided to them by the internet even normal, well adjusted people may display anti social behaviour so the chances are you are going to attract dicks. Should the world be like this? Of cause not, but sadly we should expect it and in an effort not to harm others plan for it. So that "get together", you feel the waters, get permission of the host of what you hope is a reasonably sided place before giving away your location.
Turning up to a location out of the blue and giving away its location when you have a very sizeable following is going to cause the same issues as the meet up as above but with the added effect that it's being broadcast live (so those fuck wads get instant gratification) and recorded (so they can relive that high over and over).
They only control the streamer has is seeking permission of others who they may end up causing to have a bad day (the location they are in for example) and restricting the information they give out online. I've found (cause it's what people do in the tech world) it's easier to ask for forgiveness then permission so people do it anyways and at times (not always but at times) get pissed off because those they didn't seek permission off get pissed off at them.
Personally, I don't expect the streamer to control 100% of the situation around them (what would be a meet trick for anyone who can), but I do expect them to take some measures to to protect themselves and those around them. Sure that means not streaming all the time and less spontaneous streams. But we have to also think of others around us too.
It's a difficult subject, but all good thought provoking ones tend to be.