I don’t have access to CGEL, but I am reading Huddleston & Pullum (Yes, the 2005 ed.). They categorize this in “This is infuriating” as a fused determiner-head. I think I understand their reasoning and I accept it. But on the very next page (p. 99) they categorize what in “What do you want?” as a pronoun functioning as a head. I think I understand that too. But I don’t understand why they treat this and what differently in the respective sentences.
My understanding of their view on this is that there’s a fusion that could be split up into this thing or something like it. But the same splitting could be done to their what example: What thing do you want?
So I checked their test(s) for pronounhood, but unfortunately all they address is distinguishing pronouns from other nouns.
In their discussion of what they mention that as a pronoun it’s non-personal and as a determinative it’s “neutral with respect to the personal vs non-personal distinction.” I’d say that here too this acts the same: *This just invited me to dinner doesn’t work, but This professor explains things clearly does.
So, am I missing something? Besides the determiner this, what’s wrong with saying there’s also a pronoun this? In their this example they describe it as belonging to the flavor of fused determiner-head that they label as “special,” but I don’t see anywhere where they explain that label. Could that be a clue?
(Of course, the same thing would go for that.)