Sakura is not a healer, she skill was enhanced chakra control not stamina control. Sure Gai would've helped her to over come her weakness and she would've been a great contrast to lees character, but at the end of the day he would have nothing to offer her, even though Kakashi did have a lot to offer her and look at his move set now, very Tsunade esque .
Though if Sakura spent a week with each team, and trained with them, she would be a master at genjutsu, tai jutsu would improve, and ninjutsu from Asuma, but she isn't really a ninjutsu type.