Take a look at almost any musical written in the past decade, and you'll notice that the overture -- that instrumental "settling music" which often is a preview of the songs to come -- no longer exists.
Many musicals now just jump right in to the action, maybe as a reflection of the average theatregoer's shorter attention span than our parents and grandparents before. But there was something comforting -- even if slightly unnecessary -- about overtures (and their Act II counterparts, the entr'acte) that is missed from most modern offerings.
There was a thrill as the lights dimmed, and orchestra got their one and only time to show off their talents without singers and dancers taking away from it. It would give me the few moments necessary to switch my brain over from the real world to the imagined (which was often an exciting place), and made the whole shebang feel more...well, theatrical. It would be like going to the movies and not seeing any trailers. Does it get you home sooner? Absolutely. Can you still have a good time without it? Sure. Does it take away at all from the whole theatre-going experience? Yeah, a bit.
You could say that the latest generation of Broadway composers -- Larson, Brown, Pasek and Paul, to name just a few -- whose work leans more towards the pop rock sound feel that an overture would clash with the general aesthetic of the rest of their work. A medley of melodies might feel a little disconnected to a show like Moulin Rouge, where part of the fun is the surprise of discovering the pop songs that have been turned into Broadway belters; or the biggest show in the land, Hamilton, where there's a sense of immediacy to the opening number which an overture would just delay (and add to an already 3 hour performance).
Some omissions of an overture are because they are replaced with a modern spin. Consider Rent, which flipped the script (or maybe we should say, libretto) in so many ways for Broadway theatre; it begins with "Tune Up 1" and "Tune Up 2," which is just what it sounds like, instruments preparing to play. There's no discernible melody, or preview of musical themes to come later in the show, but the quiet before the storm of the title track that soon blasts off, and the show itself which is sort of about the dawn of a new generation and the mishmash of frequencies between disparate entities.
Yet some shows that have jettisoned an overture are head-scratchers. A Strange Loop, which is about Broadway theatre, and therefore would make sense to have one, doesn't. (Ironically, the protagonist, Usher, is an usher for The Lion King, which also doesn't have an overture -- but Aladdin does in all its big, brassy excellence).
Some musicals seem to have reached a compromise; they have a minute or two of orchestration which blends into the first song. This is the case with everything from the revival of The Music Man to Wicked to Beetlejuice. In fact, the only place you can find a full-length overture currently heard on Broadway is the revival of Funny Girl; it's refreshing they didn't get rid of that along with star Beanie Feldstein.
When I go to the theatre, I want it to last as long as possible and I want to feel that magic of a door to another world opening just for me (and a few thousand other audience members). I say, bring back the overture in all its glory, and give those latecomers a few extra minutes to climb over everyone to their seats.