It would have been a sound plan if they didn't wait for ages before attacking, which led to the King's guard and the King being born. It also led to countless deaths (which they knowingly accepted) while they were waiting, which would have been prevented if they just nuked the ants from the get go.

The reason why I really don't like this bomb thing is because everyone acted so desperately as if this option did not exist. All the choices and actions look so cheap and idiotic now that we know they can just nuke the ants, and cheaply too.