Sheryl Sandberg or Marissa Mayer would be a huge win for Uber. I've worked with both of them, and know that they will bring extremely positive changes.
1. She was a good person, and went out of the way at times to make employees feel good.
2. She was a terrible boss, who would pass edicts like "our cubicle walls will be cut to 50% of their tomorrow", and pass it off as "because natural light is better for you".
3. I believed as an employee that she cherry-picked data to support pet beliefs like hiring at selected schools, banning remote work and closing satellite offices.
4. She had a preference for ex-Googlers/ex-Google APMs
She would definitely bring positive change in terms of the scandals, but any competent HR department that has the company's long term interests in mind can do that, no?
Re 4: You have your preference as well, so does Google, IBM, Yahoo and the small law firm where I work. Everyone does when it comes to hiring.
Re 4: I am sorry, I meant to complete that sentence with "when it came to hiring execs, or buying companies".
She hired some (what I saw as) very poor execs who were once at Google, one of whom got a 60m severance package for underperformance.
On the other hand, Instant Search was another edict of hers, which required months of massive planning and engineering, until it became usable and wouldn't bankrupt the company, but I'm glad she came up with it.
This was when the vast majority of the company was on git, and the holdouts were typically lazy or understaffed.
I highly doubt Sandberg would want this job, and I highly doubt that Mayer can turn around a company.