I think they already do and I think the major media outlets have been soft-pedaling leaked Clinton campaign documents. They've been reporting on them but it sure feels like selective and soft reporting designed to minimize perceptual damage to Clinton.
If they took leaked emails related to Clinton and really ran with them, it could conceivably damage her campaign, so they aren't.
Personally, I think they underestimate just what Clinton backers will tolerate and are miscalculating by soft-peddling the information, because in the long run it destroys their credibility. If they would really light her up it wouldn't make Trump look any better AND the media would regain some of their credibility.