Historically, we have dealt with belligerent non-sovereigns (e.g. pirates) via the military. How do you think treating Al Qaeda as a military threat has corrupted the military? My great worry is that if terrorism is treated as a crime, then the protections available to all accused criminals will be watered down to accommodate the needs of prosecuting terrorists. That's what, e.g., has happened in the drug war. There are a lot of bad doctrines (e.g. no-knock warrants) that were motivated by the drug war (specifically the ease of concealing or destroying evidence of drugs).
By blurring the line between law enforcement and military actions we've made it much to easy to deploy military force (most notably airstrikes) as a means to expediently solve problems. Where does that slippery slope end? When do we start carpet bombing drug cartels? We've already been invited to do that.
