Eliminative materialism goes beyond the materialist claim that mental states have a physical basis and claims that at least some mental states do not exist at all.
I think eliminative materialism is a useful concept (though I suspect that describing it as a "concept" may not sit easy with eliminative materialists). For example, one hypothesis forwarded within the eliminative materialist program is the idea that "beliefs" do not exist. There appears to be poor evidence to suggest that "beliefs" are coded in the neural circuitry of the human brain.
As someone who is easily annoyed - and occasionally offended - by the beliefs of others, I find it useful to entertain the notion that "beliefs" do not exist at all. Instead of resenting others for their noxious moral or religious beliefs, maybe I can present them with data that they haven't yet encountered. And if "beliefs" have very little physical basis in the brain, then I can abandon the assumption that others will act in a consistently noxious way by force of their noxious beliefs, thereby letting me give them the benefit of the doubt.
Switching gears slightly, even as a hobbyist philosopher, I can see how Pat Churchland's argument feels threatening to the pursuit of philosophy, classically understood. Within the eliminative materialism framework, epistemologists, for example, would have to acquaint themselves with the latest developments in cognitive science in order to make philosophical statements about the mind. I'm not sure this would be a bad thing, though it would change my conception of philosophy and upset the status quo of legions of philosophy departments around the world.