It's a tougher call than you'd think. if they just freeze themselves out, the entire White House press pool will be replaced with totally sycophantic right wing media outlets and any outlet that even whiffs of trying to report on things fairly won't ever be able to get back in.
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If we don't care about his little press hearing, he'll get upset and try to find some way for us to acknowledge him again.
He loves his sycophants but he needs the rest of us.