That's because neither Metal Gear nor Resident Evil take themselves nearly as seriously as Final Fantasy does.
To a certain extent that's bullshit.
To a certain extent, yes.
But to a certain extent, we're trying to compare a video game series that tells the tale of an alternate history where dumb action movies are real things that actually happened and have shaped human history/progress, and a video game series that tells the tale of an alternate history where zombie apocalypses happen every month or so, to a video game series about this fantastic world created by a bunch of gods and goddesses that ultimately left the world like a bubble resting on the point of a needle, where any idiot with access to a chest containing a goddess's heart can end the world simply by letting a sharp, pointy-thingy get pulled into said chest during a cutscene.
And yes, Metal Gear does try to be melodramatic when recently defeated bosses spill their life's story faster than their guts spill their lifeblood over the next 5 minutes, just like Resident Evil tries to be insightful anytime when Albert Wesker starts talking or the word 'evolution' pops up. And just like those games Final Fantasy tries to be funny with "Choco-boco-lina!" or "This is the Yuel who died while watching Friends, and this is the Yuel who died from choking on a CrackerJack, and this is the Yuel who died while giving herself a bad perm, and so on....".