Since at least sometime in the 1980s, the mainstream press has taken charges of liberal bias very seriously. Its response has overwhelmingly been defensive and conciliatory. Media handlers in the conservative movement have gotten very adept at using this as yet another tool to manipulate press coverage.
As is so often the case, Donald Trump has taken a long-standing and highly questionable practice or position and made it so blatant it has to be acknowledged for what it is.
From Josh Marshall:
[T]his year we still haven't heard who the moderators are going to be because the Commission is trying to be sure they pick people who Donald Trump or his supporters won't view as biased against him.
That is a huge, huge problem. Obviously this should always be a top priority. The moderators shouldn't have a bias against either candidate. But Trump of course sees everybody who is not obsequious and toady-ish as biased against him. Over recent weeks he's made Sean Hannity his official interviewer, like a doofus Boswell to Trump's clownshow Dr. Johnson.
He tried to set the tone with those silly complaints about conflicts with NFL games. And the only reason to be especially solicitous of these concerns is that Trump has a history of complaining. This is no more than recapitulating his strategy through life, business and this political race: start with aggressive over-the-top demands, try to assert dominance at the outset so as to engage solely on his own terms and with his dominance already an accepted fact.
In any case, they're not going to find anybody Trump won't claim is biased. No one. Literally, no one unless it's someone like Hannity or Hugh Hewitt. My concern is he's gotten inside their heads with his antics and they'll find someone who is a known softballer or someone who actually is biased in favor of Trump. More likely they will create a situation where the moderator is given a brief which makes them fall over themselves to prove they are not biased against Trump.
Perhaps we'll find out that they're just doing an extra level of vetting to make sure the people they pick didn't say something mean about Trump six months ago or something - though frankly, how many sentient people haven't made some critical comment about Trump in the last year?