I’m tempted to write a long, pompous dissertation on animism in Shinto and how this leads to humanizing inanimate objects in Japanese film in general, and from there to robots, the ultimate in anthropomorphized machines. Unfortunately, I don’t know much about Shinto and would be quickly reviled as talking out of my ass. 
Truth is, Giant Robots are a fantasy archetype, like dragons in fantasy or seductive blonde Russians, private eyes, or cheerleaders. (Another dissertation coming up!)
As Wumpus said, it’s like asking why superheros wear skintight outfits. (superheros are notoriously careless in terms of sidestream mayhem as well :)) They’re there because the shows that the creators liked had them. They also move in a roughly familiar way and have interesting shapes and silhouettes, so you can use familiar directing tricks with them. And they’re cool.
After a while, there are whole groups of animators who specialize in the tech stuff, so making more tech-stuff gets even more attractive.
As an analogy, why do so many HK actioners center around martial arts, even when they’re really fantasy or superhero movies? Because that’s what the filmmakers watched when they were learning to love movies, that’s what the audience has grown to expect, and they’re fun to watch.
Why are the weapons in pretty much all SF movies very slightly enhanced versions of pistols, rifles, and swords? (Swords?!) We can make a ship that can conquer the stars, but the best we can come up with to deal with the BEMs is a giant clunky pistol that only works if you hold it still, and shoots a flashy red beam that shouts ‘here I am!’ and seems to do less damage than a normal pistol would?
As for the rest, in any genre, fashions go in and out. The post-apocalyptic thing was ridiculously popular in the ‘80s (actually, it was almost as popular in American SF movies in the 80s) Fantasy-esque was popular during the late 90’s industry bubble, and now it seems to be nostalgia for the 70’s. Robot shows are probably more than a little over represented in US video stores, though, just cause they sell well.
By this definition, virtually every action, SF, martial arts, or western movie’s star is a Giant Robot.
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‘Typical American. Bringing at tank to a giant robot fight . . ‘