I don't even know how you arrived at this conclusion. The EFF was fighting this with education of the public, procedural maneuverings within the W3C itself, and with invited commentary to the relevant standards groups. Mozilla was also doing these things, and, contrary to what you might assume living in our tech bubble, has a pulpit with far greater reach than the EFF.
But then they implemented the damn thing--which, by the way, is not a standard yet--in their browser.
But, please, tell me exactly what the EFF is guilty of. They might have failed, but that's a very different thing.
The only way to do that would be to affect their bottom line, such as people refusing to use their browsers if they ship EME.
That would have been the only campaign with a chance of stopping EME. Mozilla couldn't lead it - it would look self-serving ("how convenient, a browser vendor wants us to boycott its rivals"). The EFF as a respected third party could have.
That would have been our only hope.
How can Mozilla kill it? It simply doesn't have the power, faced with Google, Microsoft and Apple implementing EME.
Yes, Mozilla could have taken a pure, principled stance and avoided EME. Perhaps some thoughtful people would use Firefox for that reason. But those same thoughtful people would have boycotted Chrome and Internet Explorer when they started to ship EME.
There has been no such boycott. If we - the people on the web - wanted to stop EME, that would have been the only way. Mozilla can't do it if the people don't want to.