Who is important enough, a person from new generation, capable of running the village(with help) and actually a strong ninja?
This might be Sakura, it might.
Though Sakura is one of the main characters having her become hokage would make no sense at all.
1. Lets get the obvious out of the way, she is weak. Kages are usually, you know....Kage lvl. Sakura isn't even jounin material yet. Her medical skills are great but how can she defend the village against invaders with her lvl of strenght ??
2. Being Hokage is Naruto's goal, it would be a slap in the face if Sakura got the position because she can push papers.
And I give you another thought to ponder, if not that, what is her purpose going forward?
To help Naruto get Sasuke back ( if it happens ), i thought it was obvious by now.
Also lets be honest here, logically speaking Shikamaru is much more capable ninja in every department than Sakura ( except med ninjutsu of course ), It would make more sense for him to get the position before Sakura ever could.