The design is pretty meh (at least to me, she looked cooler in the anime TBH), and the meme is dead, she's a Pretender instead of what litteraly EVERYONE FOR YEARS EVEN HERSELF HAS CALLED HER, FAKER. M'ok. Guess it makes sense, creating a whole new class which would have almost the same characteristic as a Pretender would be dumb.
But to clarify, she DOES absolutely qualify for the class.
She IS the source of the false rumors that spreaded about Alexander (height, hair color, etc...). She did it on purpose (I mean, it was her job), to blur the ennemies vision, to create a false image (ressembling hers) in the mind of others so that any ill will, curse, assassination attempt, would befall on her and let him be the king and ruler they were all following. (Hence why most informations in history books and such on Iskandar are wrong, why Waver in F/Zero was so shocked at the discrepancies between what he'd learn and the actual Iskandar)
So I'd argue she litteraly fits the bill:
She gave false representation (of Iskandar), deceiving and misleading others (ennemies) to do great deeds (allow Iskandar to continue his conquests unharmed)
The second part... Well from what I've red, she kinda does that (don't wanna spoil), becoming even greater than Iskandar in a way...
The reason why she's not summoned by Hetaroi... Het... Iskandar's NP, is cause she REFUSES the summoning. Apparently, she's super bitter about what happened after he died and the war that Iskandar's generals battled to decide who would be the next ruler. When the NP is activated, she hears the plea of summoning, but at the same time, as a (possible) Servant, she get's infodumped by the Grail, remembers the Wars of the Diadochi (Iskandar's generals), get's super pissed, and just nope the shit out of it. She loves Iskandar but she fucking HATES his army.