That’s an odd label for the view it purports to describe. The most conspicuous feature of the doctrine in question is its negative attitude toward traditional metaphysics: it is a form of philosophical “negativism” i.e. metaphysics is meaningless and should be abandoned. And what is with the adjective “logical” here? Doesn’t every philosophical doctrine regard itself as “logical”? Who would call their view “Illogical Idealism” or “Poorly Reasoned Relativism”? Doesn’t every proponent of a philosophical position take it to be both “logical” and “positive” (i.e. on the side of the good)? A better description of the doctrine would surely be “Methodological Negativism”, since it subscribes to the view that correct methodology excludes metaphysics. Or it might be called “Semantic Nihilism”, since it declares so much philosophical discourse to be devoid of meaning. But these labels don’t carry the same uplift. Doctrines often catch on because of catchy labels.
I think the phrase “logical positivism” well describes the pro-metaphysical metaphilosophy I favor: that all of philosophy is really logic (the a priori analysis of concepts), but that this conception is maximally inclusive, i.e. “positive”. Even the most non-empirical branches of metaphysics are respectable, because grounded in logic. There is nothing “negative” here! But to avoid confusion I might call this doctrine “Positive Logicism”.