Freud's objections to "schizophrenia"

Freud always remains skeptical about the name "schizophrenia"--the name that Eugen Bleuler proposed for those suffering from (what was called) dementia praecox. He even goes so far to suggest his own name instead for the phenomenon: paraphrenia. Until now, I never really understood why this odd objection on the part of Freud takes place, and does so with exceeding regularity. Then I hit upon the following paragraph in the Schreber case:

The designation chosen by Bleuler...--"schizophrenia"--is... open to the objection that the name appears approproate only so long as we forget its literal meaning.
-in Three Case Histories, Collier edition, 179

The literal meaning being, of course, "split mind." But--and here's the point of objection--there isn't a split mind here, in the case of schizophrenia, unless we are referring to how the unconscious is split. But then the term describes all psychic states whatsoever, all minds. In other words, there can only be one split:

For otherwise it prejudices the issue, since the name connotes a theoretically postulated characteristic of the disease--a characteristic, moreover, which does not belong exclusively to it, and which, in the light of other considerations, cannot be regarded as the essential one.
-Three Case Histories, 179

"A characteristic, moreover, which does not belong exclusively to it:" that means, being ruptured, having the character of something in which irruptions are mysteriously produced: this is the psyche in general, not just schizophrenia. To keep the term, we would have to distinguish between a sort of semi-conscious split alongside the split effected by the unconscious, which doesn't make sense (it makes us think of splits as having degrees of intensity, which is odd). What becomes more interesting--and what was interesting in the first place, before we called it a split and started searching for where the split is--is the question of the dynamics that could produce something like multiple personalities and all the symptoms we know schizophrenics suffer (and which also exist outside it) when they do not split the mind, but rather originate by virtue of that one split that all people have--that between the CS (or PCS) and the UCS. This is why Freud opposes the word so vigorously.
One more thing provokes a remark: "the name connotes a theoretically postulated characteristic of the disease," "theoretically" being the crucial word here. For what this implies or connotes in itself is that there is a non-theoretical assumption in naming the illness something better--paraphrenia, for example. Or, perhaps, there still is a theoretical assumption, but one which is consistent with an entire effort to theorize the mind. Freud, in short, objects to an empirical designation that in and of itself presupposes the existence of a special theoretical model: schizophrenia must belong to the entire mind, not force a new model of the mind to be applied. And not because the model Freud has is so sufficient that it should not be changed, but because this means that every illness has its own mind--something that allows no research at all.