I think a smart White House, with a coordinated and consistent communications plan, could use the daily briefings to their advantage. Instead, this White House has declared war on the media, is more and more combative and secretive, and offers contradictory messages to the American people (e.g., the reason for firing Comey and whether or not Trump is under investigation). Spicer has consistently said he’d find things out (e.g., whether the President believes in climate change) and has just not followed up on many of them. All of this makes the daily briefings increasingly challenging for this administration.
Personally, I think they should welcome the Russia probe, noting that we need to understand how Russia attempted to influence the election so we can offer effective counter-measures in future elections. I’d focus on that portion of the investigation and indicate the Administration would cooperate fully. Instead, Trump (and his surrogates) have continued to keep the collusion piece in the news by failing to disclose meetings (e.g., Kushner, Sessions, Flynn), posting ill-advised (IMO) tweets (e.g., references to “tapes”, “wiretapping”, and being “under investigation”), and offering those contradictory messages referenced above. It seems to me that the more Trump tries to move on from the Russia probe, the more he (and his Administration) keep it in the news and as a result, keep it front and center in the daily briefings. They’re their own worst enemy IMO. I doubt if “cracking down” on press briefings is going to help him beyond his base.