To be clear, as a preliminary, I am no Palin-bot. But I do not judge a person mainly by association, even if the association is family. As for being out of the public sector, that is formally true, but she has done a fairly good job of keeping herself in the public eye as well as performing public service, under conditions that I think just about anyone would consider very daunting. Perhaps you can point to something specific that you feel might disqualify her (I could at least consider something specific).
Back to being out of the public sector, I note in passing that Bolton has been out since 2006, 3 years longer than Palin. Romney has been out since 2007, two years longer than Palin. And Trump himself has never held public office at all.
Sarah Palin's track record is already thin -- both inside and outside public office. She was a small-town political figure for ten years, then governor of Alaska for less than three years. Other than that, her political career was a brief flash as a charismatic VP candidate for an old hack who should have retired years ago.
Outside public office, she's been little more than a media figure and political advocate.
There's nothing wrong with any of this, but it hardly qualifies someone to serve as the U.S. Secretary of State. I would usually consider a lack of public-sector experience an asset rather than a liability, but Palin hardly has a track record of private-sector success that Donald Trump brought to his first political campaign.
If Palin is a credible candidate for U.S. Secretary of State, then you could find thousands of successful business owners all over this country would be better suited for this role.