It certainly hasn't been a good week, although thankfully there seems to have been no notable injuries in any of the incidents.
Regarding stopping dispatch, the Guard is undoubtedly the fastest means of stopping the train in these circumstances. However, with GSM-R and the REC facility, it takes one call from Dispatcher to Signaller and the entire area can be brought to the stand at the push of a button. I am by no means an advocate for DOO, but stopping trains in an emergency is easier now than it ever has been!
Unless I've missed a really big development, dispatch staff are not routinely equipped with GSM-R handsets, and therefore it is likely that an emergency call to the signaller will need to take place over whatever the nearest handset is (which could involve running down to the end of the platform or to a control panel half way along).
It is only after the relevant information is relayed that the signaller will then be able to make a decision to use their GSM-R terminal to stop trains, which whilst relatively simple, will probably (by that point) happen after the derailed train has caused quite a lot more damage, may have injured people, and other services may be affected. Indeed, a derailed DOO service could well have been stopped by a passenger alarm eventually, or by the brake lines being damaged, but neither is going to be as rapid as somebody being able to look out of the window and stop the job immediately.