The problem being that there's no point in doing that if you don't think the outcome's going to change. Then the only reason to do it is to continue to fight the last battle and create division. Perhaps if HRC had future nationwide electoral ambitions it would make sense, but she'd be the one that would have to at least nominally authorize the requests, and it's hard to pose as a healer and divider at the same time.
This motivation was one of the problems with Gore's recount in 2000. He picked only jurisdictions where he thought he could pick up votes. That's fine, state by state, but inside a state for state-level positions it's a bit iffy. (And, no, there is no state-level election for president. States elect state representatives called electors.)
Note that in some states there's an automatic recount if the margin of victory is sufficiently thin.
There's some research--since it's an important topic--into the kinds of people that make mistakes in voting, the kinds of mistakes made in counting ballots, and their distribution. Most of it is damning for the (D) side of things, but not all. Lets just say that the pattern of voting problems we find are a combination of relying on past to predict the future, budget problems, and predictable trends from the research.