Lord of the Rings. That's where this whole argument is coming from. It's all Tolkiens fault.
See, NOBODY in favor of large-weapon two-weapon-fighting mentioned anime as its source. That's because that ISN'T its source. I know of no anime that uses this, though its possible it exists.
And NOBODY in favor of large-weapon two-weapon-fighting mentioned video games. That too is because that ISN'T its source. I know of no video game that uses this, though its possible it exists.
The source of large-weapon two-weapon-fighting is 1970's High Fantasy books. It's the Conans, Krulls, Red Sonja's, and Frank Frazetta art. It's the sculpting of lead figures to portray such characters as well. And it's the portrayal of people with massive, massive muscles who do extraordinary feats of physical prowess.
And people who are rabid Lord of the Rings fans have always tried to stay away from that type of "High Fantasy" stuff. If their campaigns are supposed to have a Lord of the Rings feel, they do NOT want half-naked barbarians with huge swords running around claiming that "What is best in life is to crush your enemies, to see them flee before you, and to hear the lamentations of their women." In fact, they don't want overly muscle-bound folks at all in their games, since the extraordinary acts in their campaigns should be surviving against the odds, not heedlessly cleaning the field with your weapon.
The problem is, these Lord of the Rings folks may be playing the wrong game. Because D&D 3e is all about characters increasing in power as they go up a level. And eventually, someone is going to be uber-strong (if they don't start out that way). And their physical strength will far surprass anything the good guys had in Lord of the Rings. And picking up two huge swords will not only be physically possible for them, but it will make sense that they will want to, because it shows off their stength, just as the rogue will want to show off their dexterity, and the Bard their charisma, and the spellcasters the power of their spells.
The rogue is going to start doing tumbles that are physically impossible, and will appear like Jackie Chan or something from Crouching Tiger, Hidden Dragon. Are you going to disallow those also, because they don't meet with your Lord of the Rings driven expectations of your player's behaviour? Your arcane spellcaster, for that matter, is going to start flying while invisible and throwing fireballs from a distance, also highly un-Lord-of-the Rings.
And I agree that none of this is what Lord of the Rings is about - but it IS what D&D 3e is about, as character power grows.
The problem isn't monkey-grip. The feat is not overpowered, it isn't any less physically possible than what the other non-fighter characters will be doing at some point, nor is it any more or less silly than what those other non-fighter characters will do at some point. The problem is monkey-grip isn't Lord-of-the-Rings-like. And that IS a problem, if you are going to insist on DM'ing the wrong role playing game.