Her H-Index was 10 or 11 before Google removed it. By comparison Summers is 138. https://scholar.google.com/citations?user=yX255OoAAAAJ&hl=en
My take: I think Gay was one of several up and coming internal candidates which Harvard keeps in the wings for bigger things. She had capably proved herself as FAS Dean, much like Faust oversaw the Radcliffe Institute. The search committee thought Gay would be ready to lead the University as an experienced administrator, and ignored or overlooked the academic red flags.
Worse than mine and I don't even have a college degree. :P
Stack committees with myopic pointyheads, strategize departmental budgeting and approvals to keep them in a state of vague paranoia and conflict with each other, and enjoy having a divided, distracted, powerless faculty body?
Look up who's on your state education boards and test the saying, "never let academics decide policy."