What new shows (not a revival) since 2000 have had "traditional" overtures or even any overture? Legally Blonde has a less than one minute intro of music - but not what I think of as an overture. The Light in the Piazza has some wonderful intro music as well. Why aren't there more overtures? And which show is credited with starting the "trend' of no overture (which goes back quite a ways)?
Newsies, Ghost, Matilda, Honeymoon in Vegas, Bring It On, A Christmas Story, Chaplin, Wonderland, Women on the Verge of a Nervous Breakdown, Elf, The Addams Family, From Here to Eternity
They all have an Overture of some kind, though a lot of them are less than a minute long. And these are all 2010-present.
I took loliveve's advice and did a search on my own iTunes (I have over 1400 cast recordings), and since the year 2000, there are 46 overtures from new musicals (accounting for human error; although some are "jukebox" musicals, and also I make no claim to have every new recording produced). As the BoyfromNC mentioned, most of them are very short (I blame attention spans of the masses and television for this).
The list (excluding what has already been listed) includes: The Beautiful Game, The Full Monty, The Witches of Eastwick, 3hree, Thou Shalt Not, Urinetown, The Producers, Seussical, Thoroughly Modern Millie, Chitty Chitty Bang Bang, Amour, Bounce, The Color Purple, Little Women, Spamalot, Curtains, Young Frankenstein, The Little Mermaid, Shrek the Musical, Wonderland, A Little Princess, Top Hat, Gentleman's Guide and Honeymoon in Vegas. Out of all the overtures from this century I would say only Honeymoon, The Light in the Piazza and The Producers are full-length overtures that include a good sampling of the evening's upcoming songs (although I remember thinking Drowsy Chaperone also had a good selection, it's only 2 minutes long).
As for the OP's question of what show started the trend, at first I was thinking Les Miz's lack of an overture may have started it (technically the Broadway recording lists an overture but it's roughly 30 seconds of a recurring melody). But I think overtures were really big in the 50's and 60's and were petering out in the 1970's and 80's. So I guess I can't really pinpoint it. Company had no overture and was from 1970, maybe that started it?
"Contentment, it seems, simply happens. It appears accompanied by no bravos and no tears."
WEST SIDE STORY's lack of an overture in 1957 was probably the first in a major Broadway musical.
I think in modern times it depends solely on the style of the show and the discretion of the authors. Shows like THOROUGHLY MODERN MILLIE and A CHRISTMAS STORY are set in the past with period scores so it seems fitting to have an Overture since it was common then. LIGHT IN THE PIAZZA has a lot of operatic influence so a traditional overture also is fitting. Of course there are still some period shows with period scores without them (GENLEMAN's GUIDE for example) so it's really up to the writers.