And how will a system like this handle news or reports about events that challenge our world view?
Not everything takes the form of Trump saying random outrageous stuff that is easily verified/rejected.
Also, you may say that "Fact checked" is just an additional data point to judge whether to trust an information source, but you know as well as I do that lazy people (most people) will start thinking that "Fact checked" means truth and "Not fact checked" means lies. Even more so on Facebook.
I think, in the long run, these systems will be detrimental to peoples' ability to judge any information themselves. This is a problem for democracy.