(sorry, this turned in to a thinking out loud / brain download...)
I don't see why any contestant should be sent home just because they're not popular enough to win (and Saara's not the only contestant in that position), and with Saara I don't think there's any misery to be put out of.
I'm not sure I would have selected her for the live shows (as if it would ever be up to me, ha!) because her appeal is quite narrow.
I think you can see Simon having a "is she right for this show?" moment during her audition whilst Louis and Nicole are entranced, but I think he respects her and genuinely believes she needs the platform (aside from any "how can she make me more money?" stuff).
I can see where are people are coming from with "shrill" and "cold" etc. because her voice is cut glass theatrical (and "unfair" too, her experience advantage is obvious) but I like Saara and I like being able to just enjoy someone singing without having to worry about parts that will make my ears hurt.
However, I can see how her professional sounding vocals might alienate or don't connect with people because they're not that interesting or fashionable (but maybe they're going to become fashionable again).
I think she's in a strange place really; she's much more than a professional karaoke singer or a "stars in their eyes" whatever (she's a fantastic singer), but seems to lack the identity or whatever you call that special thing that makes people with great voices in to stars.
But I'm glad she's on the show (if only, paraphrasing what Simon said at her audition, to show how it's done) and really don't care if any more contestants get sent home instead of her.