They were rather constrained with regards to Bechdel's test by having to work with only one existing main cast female member. Adding Chapel would've been a stretch with regards to her and Uhura having a reason to talk to each other that didn't scream "Look, Bechdel's Test moment!". Maybe adding Rand would've enabled a pass, but with all the lead characters so young and inexperienced, a Yeoman wouldn't have worked unless they played it opposite and had Rand be the equivalent of the grizzled Sergeant who's the experienced one relative to the wet behind the ears main crew. And that would've made her have too big a role relative to the plot of seeing Kirk and Co. earn their (ridiculously over-promoted) stripes.