Never said Sakura couldn't, it simply works better for Tsunade's team. What can Sakura boost? Naruto's FRS? And allow Sasuke to hold up his V4 Susano'o longer? That's really about it, and both of which can be dealt with. Tsunade is a far better medic, and on the other hand can boost an array of techniques in Jiraiya's ninjutsu based arsenal. As well as Hiashi's air palms, that can already be used to knock away a Jubi's tail on his own. Zetsu Orochimaru can use any technique Zetsu has shown, which includes Mayfly.
Your lack of knowledge on the manga is showing. Neji and Lee are absolute none factors in this caliber of a fight. So it's just MS Sasuke, SM Naruto, and Sakura Vs Zetsu Orochimaru, SM Jiraiya, Tsunade, Hiashi, and Gai.
It's not a balanced match, when you consider everything the masters have to offer while the students literally are relying on camping inside a V4 Susano'o, else get stomped by 7G Gai. Susano'o goes up, and so does the Rashomon gates to protect the masters frontal from anything and everything. 7G Gai and Hiashi's air palms boosted by Tsunade keep V4 Susano'o at bay long enough to open a window for Zetsu Orichimaru to Mayfly underground to release spores from underneath Susano'o and into the pocket that Sasuke, Naruto, and Sakura reside in. All the while SM Jiraiya is prepping Gama Rinshō behind the Rashomon gates, which leads to the the GG as Susano'o doesn't protect from sound.
Edit: Actually, it's the toads that are prepping the genjutsu. Jiraiya is free to use Yomi Numa under Susano'o for added insurance. Orochimaru can go 8 Branches after the spores. This is rape. V4 Susano'o can not handle all of this at once and be fast enough to interrupt Gama Rinsho prep.