Sakura couldn't even talk to her daughter without losing her temper via faced questions about her marriage and people think she can run a Village? This girl faints at the sight of her house breaking and people think she can handle the stress of running the village whilst raising Sarada?
Sakura fan's are delusional.
So what? Sakura has always been shown to be level-headed in situations that aren't for comic relief, like running Konoha hospital during the pein attack at the age of 16 or using her reserves to fully recover Naruto and healing the entire a alliance alonez. She's only ever bursted on Sarada once and y'all acting like it's a common occurrence?
Sakura is one of the smartest people in Konoha, the 2nd strongest due to Sasuke's absence and has been said by Boruto to be a suitable replacement for the hokage status she's also a very hard worker mastering Byakugō in three years, and unlike Tsunade and Naruto she would be excellent at paper work. She was also stated by Kishimoto to be the best ninja instructors amongst her team, so she's definitely has the qualities of a leader.
That's why.