Yeah, but show me the part in E Pluribus Unum, where she actually saysythat she became a real Heroic Spirit that entered the Throne of Heroes.
She only said, that her manifestation as a Servant is a special one, that the incineration ended the Land of Shadows as well, which leads to Shishou being basically “dead”.
She even said so herself with the quotation marks, indicating, that she never actually died, which would be a criteria to actually enter the Throne.
Her, being summonable in America, is because there’s no other living version of her in existence anymore.
You said it yourself: UBW treats Shirou and Archer as two different beings, because Archer is in fact the ideal Shirou aims to be as well as a Guardian. It’s something that has yet to exist.
While Scathach on the other hand isn’t any different to her normal self. The summoned Scathach isn’t a guardian, nor an ideal or anything the like. She’s something that ceased to exist.
That’s why she identical to Merlin. Gilgamesh was able to summon Merlin, because he didn’t exist back then.
Same with Arturia, which is why I brought her up. Technically she died, which would lead to her spirit core being recorded by the Throne of Heroes, which again, is only because she made that vow, as explained in Fate.
Even the game’s mechanics work that way: You can’t fight with two Servants at the same time. There can’t be two versions of the same hero at the same time. (Friend support aside - that’s something else entirely).
So even IF Scathach would have been recorded by the Throne, she wouldn’t be summonable, because there’s a version of her in existence during all time until humanity has ended.