In other words, it's not even a question.
Just what the public wants: four more years of feckless investigations that go nowhere.
That depends, though. The investigations have, or don't have, an effect depending on the sort of coverage the media gives them. As cynical or craven or partisan or pandering as they may be, the media always have reasons for reporting as they do.
The thing about Hillary Clinton is, she's an awful human being: utterly dishonest, relentlessly calculating and cynical, recognizably corrupt, and in all ways the worst possible vessel for whatever "progressive" hopes the media and liberal upper crust may cherish.
As a matter of power politics, the Democrats could well decide to dispense with Hillary Clinton. The Obama wing hates her; and her very ghastliness stands to wreak havoc on their future chances. There's a good argument to be made for getting rid of her sooner rather than later in favor of Kaine, whose anonymity is a virtue -- they can paint his portrait in the best possible way.
As a matter of business, the media desperately need some way to re-establish credibility with the general public. How better, than to do the same sort of investigative journalism that brought down Nixon, the president who, in demeanor and behavior, is closest to Hillary Clinton?
One could imagine those two dynamics coming together.
Not that they will, mind you, but they could.
It may all be moot, however, if and when Hillary Clinton's health issues become too obvious to ignore.