I have a simpler theory that Beyond was simply the least appealing to the general public, who make up the majority of potential cinemagoers.
That is supported by the fact that Into Darkness attracts far better user scores than Beyond - see IMDb, Metacritic and Rotten Tomatoes - and that Beyond had a substantial drop-off after the first week, suggesting poor word of mouth. Into Darkness also did hugely superior numbers on disc sales.
I knew Beyond was in trouble from the first review I heard which said it was "one for the fans" - by implication, therefore, not for the vast majority of people who go to movies.
I daresay its failure is more due to that perception, plus poor advertising, a lack of a recognisable addition to the cast (contrast the prominence of the popular Cumberbatch in Into Darkness' advertising with the unrecognisable Elba in Beyond) and a lack of engagement with viewers.