The name itself has an ominous ring. We know what what eliminativism means in politics and it isn't pretty. Eliminative materialists are not bent on genocide, but there is something oppressive and colonialist in their worldview, how they privilege a supposedly objective science over subjective lived experience (see bird's eye view vs. frog's eye view). I would rather not have my folk psychology eliminated, thank you very much.
Systems may be observed from the outside, or from the inside. We call these objectivity and subjectivity.
Our culture tends to value objectivity, with good reason. Subjectivity is as common as dirt; everybody does it; but objectivity is an achievement, requiring schooling, training, and institutional practices like journalism and science.
It seems to me that subjectivity and objectivity need to be balanced and integrated. Too much emphasis on the objective, and you get eliminativism or gradgrindism or Rationalism. Too much emphasis on the subjective and you get the rancid aspects of postmodernism and whatever it is that seems to afflict the younger generation, a kind of toxic emotional entitlement.