I wouldn't say this is entirely because the writers favored these three, but I feel it partly has to do with the fact that those three are the main representatives of important alien factions Shep has to deal with (hence all of the cutscenes) and they just happen to be romanceable squadmates as well.
Well, Liara does have a little advantage compared to other two, since she was envisioned as a romantic interest for PC from the start of the trilogy. Garrus and Tali got added because they were so popular. Which is great and they are both great romances in their own right(won't go into how I feel about Tali's romance, since that is purely subjective), but Liara is the only one with a romance spanning all three games. Proponents of canon romance theory often cite that as a good evidence for Liara being that one canon romance. If I'd believe in it, that would be as good as evidence as any.
Personally of course, Liara and FemShep are canon for me.
Talking about a canon romance would be relevant if we were talking about something like the feature film adaption of ME, which would probably feature MShep romancing Liara. That's just probably what the writers would've wanted given how they wrote Liara, and having the heterosexual male protagonist romance a beautiful humanoid alien woman is just the most marketable for this genre (much to my personal disappointment lol)
MShep with Miranda/Ashley is easily marketable, too, but IMO making a feature film about that would be wasting the unique 'exotic' charm Bioware has created in the ME universe regarding cross-species relationships that have depth.
Funny you talk about a movie adaptation. I've made a post some time ago, where I described how I see it happening. If you're interested, give it a read, I'd be interested in knowing what you think.
But you make a good point. Marketing MShep/Liara caters to the most typical audience(young, heterosexual male gamers), as well as capitalizes on one of the unique appeals of MEverse. After all, xeno romance is a big thing and while I believe there will be more important things to be had in the movie, it's an easy way to show something different and easily recognizable.