Even though Sasuke did deduce this on his own as well, Karin was able to figure out Izanagi, and overall her sensory ability allowed Sasuke to get to Danzo as quickly as possible (even though she also was not enough to get him through the Summit alone and Tobi's interference was what really set up their fight). There is also the convenience of the bite-healing/chakra transfer over Sakura's healing (and she was not confirmed to have katsuyu at the time either iirc, which further dampens her utility).
Ultimately, Karin's healing is more convenient/versatile (and she has more chakra), and her sensory abilities are ridiculously good (this is what really separates her from Sakura and it cannot be emphasized enough).
Sasuke himself said that Sakura was better than him at genjutsu know how and analytical skill, in part 1. And that skill have sense improved, due to the sasori fight, she is able to read through attacks.
Sakura would've know that something was up with Danzo, she wouldve found it out. And her knowledge on Hashirama cells would've been useful as well. Also she wouldve warned Sasuke about his arm, leading him to use his sharrigan to see the chakra in the arms.
OKay since this is during that time, KArin has Sakura over the sensory.
But, Danzo would've have gotten far with Sakura replacing Karin because the 4 Kage would probably be sleep, or dead in that little space. Sasuke and Sakura would be a deadly combo.
Sakura had the healing ability and chakra transfer technique at the time, Katsuyu isn't really needed (aside from sensory).
Worst case scenario if Sakura was fighting along with Sasuke, Danzo probably would've tried to use genjutsu on her to fight against Sasuke....which probably would Failed because Sakura would never hurt Sasuke
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