Metalcore is kind of an ambiguous genre now. So many bands have abandoned virtually all hardcore elements that it makes little sense to call these bands metalcore anymore. Most of what some people call breakdowns aren't true breakdowns.
Check these out:
STRIFE - BLISTERED (true breakdown from 1:35 on, basically)
EARTH CRISIS - PROVOKE
Strife and Earth Crisis are the kinds of hardcore bands that really started the whole metalcore thing. They did it first, though it was still called hardcore back then. These were hardcore bands that had a good dose of metal in their music, but still retained their hardcore style. What came after, and what mainstream knows as "metalcore," is pretty much metal with virtually no hardcore at all. What is known as a breakdown now is usually just a bridge where a solo would normally go, but the band's guitarists are too shitty to play.
A breakdown is pretty much made for the live setting. It's that riff or riffs that you can imagine hundreds of people just grooving to. It makes little sense now, as the live climate has changed from back in the day. Mosh pits are now human blenders filled with meatheads and six-days-a-week-emo fags trying to act hardcore on Saturday night. It's not the same anymore. A breakdown doesn't go over well in today's live setting because of the mindset of this generation of fans.
That's not to say there isn't a ton of great metalcore bands out there. There are. If you want true metalcore, though, don't look to the mainstream.