That sounds awfully close to claiming that anyone from "the press" ought to have the right (?) to White House credentials.
I'm sure CNN realizes there's only just so much room for representatives of various news organizations. Not everyone can get in. A reporter from our local college newspaper for example, although a dedicated journalist, probably can't get credentials. Seems to me White House credentials for White House provided press briefings in the White House ought to be controlled by, well, the White House. I don't think any news organization can claim a right or entitlement to such credentials. I would be particularly skeptical of such a claim by a "news organization" that had shown such obvious bias that mostly what they put out is well-spun propaganda message and agenda, not news.
I think CNN is going to have to show some inherent right to claim a set of credentials over and above all other news organizations that don't currently have representatives there. Basically an impossible task. They (CNN) are no better, and if falling ratings are any indication probably significantly worse, than any other news organization.
The only solution, then, would be a lottery.
Cnn gets in. Just not the dh
Consider what happens if Trump just decides to cancel the whole idea of press conferences, and goes with one on one interviews with selected reporters. And if you piss him off, you don’t get selected again.