Sound design as the musical score is a trend in trailer editing that is still going to strong, but probably less well known than something like the Inception BRAAAAAAAM sound. This is when either the entire trailer or a section of a trailer is driven by the sound effects to the point that it becomes music-like in its function.
Syncing sound effects to the music is nothing new in trailers; I do it all the time, and just about every trailer editor does it. The simple reason is that it's just very satisfying to hear/see things in sync. Just watch a reality TV show like Hell's Kitchen, just about every camera move, glance or movement is accompanied by a sound effect. I talked about Mickey Mouse-ing a lot in my post about what I think about when editing.
The difference lately is a lot of trailers are drawing far more attention to themselves by doing things like dropping the music out entirely during these sound effects montages. Some recent trailers that did this include trailers for Sleepless, All the Money in the World, The Maze Runner 3, Kong: Skull Island, and Bleeding Steel.
I haven't experimented with this sort of editing much, but it inspired my editing of the Quadrilateral Cowboy trailer; that editing choice was also out of necessity because I didn't have any music to work with for the trailer.
Further working our way backwards in time, the trailers that use this sort of style manage to better integrate it with the themes of the film.
The teaser for the Ben Affleck film The Accountant repeats certain sounds like the car windshield wipers, a puzzle being assembled and fingers drumming. The images imply that Ben Affleck's character has some sort of obsessive compulsive tendencies, so the repetition and patterns play into that nicely.
The trailer for The Big Short also starts off with a bit of this stylistic sound effects editing. Here the sound effects create a suspenseful feeling in keeping with the talk about the housing market being a ticking time bomb.
But the first example I can think of this style of editing (and in my opinion, the most successful) goes back to the trailer for A Serious Man, which was made by Mark Woollen & Associates. The trailer starts with a thumping sound which is revealed to be a head being smashed against a chalkboard. Lines of dialogue, a woman clearing her throat, a car crash and other sound build up the intensity until a climax when it all cuts out.
I still haven't seen the film, but here's IMDB's capsule summary:
"a Midwestern physics teacher, watches his life unravel over multiple sudden incidents. Though seeking meaning and answers amidst his turmoils, he seems to keep sinking."
Just from this synopsis alone, the trailer feels thematically appropriate. Regardless of whether or not the moments in the trailer are one of these "multiple sudden incidents" the layering and combined build up of these audio elements do give a sense of overwhelming circumstances that a traditional musical score might not.
Using the themes of the story to motivate this editorial decision was a brilliant idea that makes the trailer a nice companion piece to the film. This is what I think makes this trailer the most successful of the ones I've discussed here. There's nothing wrong with editing something for the sake of flourish and style, but I find it most worthy of note when the editing of a trailer can tie into the themes of the story