You have a rather slanted view of the effectiveness of law enforcement. If a criminal does not fall into their hands, cops are just about 100% ineffective. When was the last time a housebreak or mugging was solved in your town if it took more work than driving to the nearest crackhouse and rousting the usual suspects? What on Earth would inspire you to "trust" law enforcement in a case like this where they have amply demonstrated an ability not to just fail to solve it, but to screw it up big-time.
As to why I think the shooter is here illegally, one reason is the phone call. If we do not know where the call originated, it originated overseas in a hostile country, or hostile area of an underdeveloped country.
I bet you most LE agencies have high conviction rates in relation to burglaries of residences...