I think I see what you are saying: "Euhemerism" is the idea that the gods were in fact actual men, whereas for Carrier's usage the euhemerizers weren't even looking to find the "actual men" behind the stories. It's a fair point. I'm not sure how relevant the motive behind the process is, though. For me the sticking point is that euhemerism was about rationalizing the myths of the gods as being about ordinary men (which is what Euhemerus was accused of doing, for which he was accused of 'atheism'), while Carrier's idea that this could lead to stories about godmen instead of ordinary (but heroic) men simply doesn't fit that definition.
I don't think Carrier needed to point out that a mythical Jesus would have necessarily been an example of what has been called "Euhemerism". He (Carrier) is just putting a name to the process by noting that from many centuries before the time of Paul, religious fanatics in that region (almost everyone was a religious fanatic at that time), had created stories about gods, angels, demons etc., saying they had done all sorts of quite detailed things on Earth, but where in fact those figures were all actually just imaginary religious beliefs about heavenly spirits.
All that Carrier needed to show, is that at the time it was common practice to create realistic sounding stories of how various gods and other heavenly creatures did all sorts of detailed things on Earth, when in fact these gods etc. were actually very clearly what we would now all understand to be imaginary spiritual beliefs. You don't need to say it was "Euhemerism" just to point that out. Although perhaps Carrier felt he had to identify the practice in that very specific way, simply because he was writing a book which his publishers were intending to offer for popular sale in high street bookshops ... ie in the same way that commercial publishers would probably have no interest in any such book unless it
did present some specific myth theory (i.e., the publishers would probably have no interest in publishing books which merely pointed out why the evidence for Jesus is so far from convincing ... although that is in fact all that any of us really need to say about a HJ).
Another factor which, iirc, Carrier did not highlight in his books, is that it should be quite obvious that in biblical times, preachers like Paul (and probably everyone else) did not distinguish in any clear way between fact vs fiction. Instead they certainly believed (for example) that the gods and other heavenly figures were absolutely real. In fact, even today in the 21st century, billions of Christians (and Muslims) believe that God is literally a real person ... when any sane educated person would now have to accept that God almost certainly does not, and actually cannot, exist in any actual real form or sense.
But none of that should be a surprise to anyone. Just step back for a moment and look at the context of the time and it's wider picture - if, as seems quite possible from his letters, Paul was describing belief in a spiritual Jesus rather than any actual human preacher, then it's hardly surprising that later preachers in the gospels (for example) would preach to their congregation with scenarios and stories that told of this messiah doing and saying all sorts of wondrous things with his faithful followers on earth. That's just a quite obvious way to make the beliefs come to life in a way that people of the time could understand, and in a way which they could easily communicate to one-another to spread their religion. And especially so where at the time, people clearly did not distinguish any difference between what we would now call reality vs. fiction. To people like Paul, God was absolutely a real person ..., and a divine revelation of Jesus meant that Jesus was certainly a real person too. And that was never in doubt for any of these people anyway, because it was all true by divine prophecy in the OT since at least 500 BC (probably since 1000 BC).
Personally I don't have any particular allegiance to Carrier's specific form of myth theory. Except in so far as various elements of what he explains are obviously correct (e.g. just things like the unreliability of the biblical writing and also of the hearsay mentions in 11th century copies of things like Tacitus and Josephus, the similarity of various points to what was said for earlier dying-&-rising gods, and perhaps also the description of how in the writing of Philo it appears that the author was interpreting Jesus as a spiritual pre-existing messiah from what he (Philo) believed was written long before in the book of Zechariah, etc. etc.).
But it should be obvious, irrespective of any books from Richard Carrier, that since long before Paul and the gospels, religious people in that region had been creating stories of imaginary heavenly gods, saying that in their stories these gods had all been doing and saying all sorts of things on the Earth. And it now seems that same idea probably extends to OT figures such as Moses, Abraham, and King David, who are now widely thought even by biblical scholars, to be imaginary figures, but where they were given a quite detailed earthly narrative describing all sorts of realistic-sounding tales about them.
