Eh, there's kind of a hole in that idea. If you recall, the Japanese government already knew about the upcoming invasion because they passed the PSE Law a looong time before the 7 days occur to get their giant Yamanote microwave up. Which indicates that the Law side did tell the humans what was coming (because the Shomonkai and Chaos warning them about the demon invasion is fucking dumb since that basically guts their plans), except the Nipponese officials decided it was a better idea to make a giant, jury-rigged, demon-killing microwave oven instead of making a fake disaster to evacuate the Yamanote circle on the days before the Shomonkai start their plan.

And judging from the actions of the government in-game, they're dumb and incompetent enough to do that all on their lonesome.