Never really understood that argument myself. Having a fan who cares about things like continuity is always going to be preferable to me than some random media tool who is doing it for the cash being the writer.
Having fans in charge hasn't done the revived Doctor Who any harm.
Depends on the fan and the franchise. While Abrams was a casual fan, other members of the "Supreme Court" are more "serious". So its not like Star Trek is being run by folks with no knowledge of continuity.
Doctor Who's timey wimey nature lends to a looser continuity. And fans who come pros don't tend to be the OCD types.