To me Press briefings are not "news". They are a venue where people get to ask, "the White House" through the US Press Secretary about "the news" and the President's position or clarify the President's position on issues in the news.
Arguably, it shouldn't even need any members of "the press" to be present. All it really needs is a room full of people who can ask good questions. A streaming video of that briefing could then be made available to all media outlets.
It is hard to argue that many podcasters are more qualified than most journalists to ask intelligent questions on the news of the day in fields in which they have expertise.
Nothing is more irritating than to watch a journalist try to play gotcha instead of helping the public understand what the position of the administration is on a certain issue.
If there were a better way to pick the audience during the briefings than the White House Press Corp we should explore it. For example, I would much rather have someone like Alan Dershowitz in the audience asking questions regarding what the White House's position on birthright citizenship is... then some journalist with no history in Constitutional law or someone like a retired border agent asking questions on how Trump intends to secure the border, than a journalist.
The Briefing room should be comprise of people with subject matter expertise on the issues of the day asking questions to clarify matters that were not clear from previous statements or policies issues by the White House.