The main point behind all this is to fulfill the deal that gives us Taiga back
I can see Shirou wanting to save Rin, if only by taking her out as a Threat by terminating Artoria and BB
But I think Rin has been doomed the moment BB captured Taiga, because it became very personal for Raiga
Rin dying will totally affect Ayako and Taiga, but seeing that it was Raiga who pushed for it, very likely they will put all the blame on him.
Neither of our Servants would care for what is going on, and even EMIYA may not begrudge Shirou much, seeing he was more than okay betraying RIn in UBW, and both Sakura and Taiga are at stake
And Sakura will be affected, but I don't think it would be too painful for her. After all, Rin was more than okay not seeing Sakura as her sister, not even asking how she was doing with the Matous.
But certainly this whole thing is going to weight Shirou down. Just like Shinji.
There are many ways to punish Rin without killing her. Some worse than death for a Magus.
I'm relatively fine with her dying if Raiga gets to her first, or because during the talk Shirou deems it the best choice, hell, even BB Killing her for whatever reason.
But if it's the scenario you imagined, with Taiga saved, Rin and Shirou being relatively cool with each other, killing Rin would just make Salter not give a damn and go out with a blaze, causing more death in the process or Go to Kirei, which is arguably worse, and Let BB on the loose, which is even worse. Ritsuka would know, and I doubt she won't tell Shirou.
Ugh...I guess I just want for something to actually go for the better. We already have a Monster, Kirei, Angry Matthew, BB and fricking Sauron (granted, Shirou does not know). We need all the help we can get, and Shirou or Raiga killing a potential good ally doesn't really help with that in the long run.
Besides, Shirou would help Rin if he saw her willing to be better.
That's the difference between her and Shinji: Shinji doesn't try to be better, and does not care of the pain and death he causes. Rin, who IS a good person at heart, does and we as readers know, because of interludes, that she already regrets doing what she did both directly and indirectly. I genuinely think it would be more interesting to let her live and try to redeem herself.
And, funnily enough, She's right now in a similar (yet so very different) position to Sakura:
-She lost her home
-She has basically been abandoned by everyone
-Her only parental figure only ever brings more pain to her
-Causes Saber to go Alter
-Indirectly Causes innocent death
-Kidnaps Shirou's Sister (Illya in Sakura's case).
It would also be fun for it to be Sakura herself to insist on helping Rin, should she get better soon, just to show that she is the Stronger and Better person.
Tl;dr killing Rin off is edgy AF, let her live to pay for her sins. Make Fuyuki Great Again, because what's happening in London will bite us in the butt.