Actualy from memory, being a POHM (British).
The bio box [booth] started to creep in about the late 50's. This was caused in Britain, primarily because a lot of live theatres had been adapted as picture houses. With the advent of TV & a spreading coverage by the BBC through out the regional areas. Forcing theatres to look to films as way of staying in the black, rather than closing thier doors.
The bio boxes were for the most part a partitioned room, gaffed together to house the projector & film gear.
Later in the 60's when rock 'n roll shows needed venues to perform for the teeny boppers. Picture [theatre] Houses were the obvious chioce, as the film screen could be flown out & quickly converted back to a live theatre, to acomodate the shows, then reverted to a picture house once more.
For the most part it was easier to establish a purpose built bio box & control booth, in the FOH, as lighting technoligy had gone ahead in leaps & bonds. Thus retiring the old Sunset Row & other types of large dimmer controls from backstage. this was how it came about in Pohmyland [Britain] & I'm sure it was much the same there.
However the SM remained on the PS [Devils Side] as in most cases this was the side of the stage that large dimmer controls were located. Leaving the OP area for the Fly system.
With better communications being installed it was a natural progression for the SM [DSM] to be drawn to calling the show from the bio box.
I doubt it was just a traditional Pohmy thing, but more purely one of logistics, as the Promter, lighting control gas table & later the electrical lighting dimmers & Light Operators.
Well that's how I remember it happened with theatres in Britain, It certainly happened this way with my Great Uncles Theatre [Tyne Theatre & Opera house] in Newcastle On Tyne NE England. Which became the Stoll Picture House in the 50's, then converted back to the Tyne Theatre in the 90's, after being used as a Bingo Hall for a number of years.
{So I believe, there is still reminants of the gas pipe lighting system there, used in the early 1900's & even relics of the first electric lighting system [water dimmers (P*ss pots)] that was installed later on in that time.}
I don't know if this helps, but it may clarify some of the transitions in theatre operations.