Not even Minato could have improved upon Sakura of Part I.
Chakra control aside (she doesn't need to be taught how to refine it) - he's a creative genius and Sakura isn't.
She hasn't shown any skill, affinity or will to develop her own techniques, or in anything outside what Tsunade has taught her herself.
Genjutsu? Minato, as far as I can recall, doesn't have any particular skill or explicit interest in the art.
Fuinjutsu? Despite her chakra control and intelligence I can't recall Sakura showing any particular skill or interest in this herself.
Taijutsu? Their styles are opposites, ill suited to each other.
She's apparently Water/Earth natured and Minato is Fire/Wind/Lightening :lol
Though I get why Rin is used as an example, that in itself is hardly fair - war time and all that. Between Minato being required for other missions, Rin's time outside team training (I imagine) would be largely spent in the hospital or assisting them in general.
... Sakura on the other hand sat about and did nothing to improve herself. She relied on her academic skills to see her through and neglected her physical training and her apparent affinity for genjutsu.
Had she asked Kakashi, straight out - "Train me in genjutsu!", I don't think he would have said no. I think he would have called in a favour to have someone better train her in the art perhaps.
They are genin - not academy students - and Kakashi refers to them at this point as soldiers. She has to take initiative to imrpove herself, to push herself to get stronger for valid reasons... something she's wholly without when she was Kakashi's genin student.
Should probably keep in mind that Kakashi's own experience as a genin/chunin was vastly different from their own - what he probably expected was Sasuke and Naruto's drive/determination and dedication to training.
Sakura, she fell so damn short it's laughable - what sensei should reward that behaviour with training?
... she didn't deserve it, training and techniques like that - coming from an elite jonin like Kakashi, should be earned by those who want to learn.
So Sakura remained an untrained dumbass until after the Chunin Exams.
Kurenai had the best skill set to teach Sakura, hands down.
She also had the right mentality regarding taking your training seriously - kunoichi pride and all that. Would have loved to have seen Kurenai pick that girl apart and break her out her fangirling. But alas, it was not to be and we had to suffer through 700+ chapters of her stupidity.