I think of all the factors, the release date was the key stumbling block. The studio obviously had lower expectations for Beyond, based on Into Darkness’ performance, the mid-July release date and the budget information (shooting in Canada, a lower dollar figure for the actual production of this film) which tells us the studio was looking to control costs and reduce their risk. I’m sure the studio was hoping for a Mission: Impossible - Rogue Nation performance (solid opening, good legs = $195 million), but with Bourne and Suicide Squad in the weeks following, competing for the same audience, Beyond was going to have two weeks of significant drops. (I would point out that M:I benefited from two disasters in the same space opening after it, the Fantastic Four and the Man from UNCLE). Beyond did stabilize after those two opened, but the release date cost this film millions. It’s not hard to see why it happened, they moved back to avoid and give breathing room to ID4 (which was expected to be huge and ultimately tanked) and didn’t want to go up against Ghostbusters (which had a lot of buzz going for it). This was a tough summer because we basically had a tentpole every week. It might have been better to take Teenage Mutant Ninja Turtles: Out of the Shadows’ June 3 date. The following week openers were Warcraft, Now You See Me 2 and the Conjuring 2; you could make a case that Warcraft targets the same audience, but I don’t see that opening hurting a second week of Star Trek.
There’s a lot of criticism here about the marketing campaign, and I think there are a few ways to look at it. The studio really downplayed the anniversary aspect of the film, which quite frankly is its only buzzworthy selling point, and instead sold it as a slam bang, good time action adventure. The problem there is you create an impression that the film is inconsequential (which was pointed out in several reviews) and that’s a tough sell for a tentpole film in today's market. That being said, you could make the case that the studio did a tremendous job opening a generic, buzzless, inconsequential film to $60 million on its way to $165 million domestic. At the very least, they avoided a potential disaster (the film is a disappointment and failed to breakout, but it's not a bomb) and the results prove there still is a significant audience for Star Trek.
I do wonder if a November/Thanksgiving opening (maybe Arrival's Nov. 11 date) after a steady build starting with the September anniversary wasn't the better play, in an effort to replicate Skyfall to some degree. July was likely a safer play; there's risk in a November opening given with Dr. Strange and Rogue One and the smaller holiday release window. Also unsure if the contractural 6 month buffer with CBS over Discovery was a factor in Paramount's thinking.