I'm a little uncomfortable w where this is coming from, and why, as well as where it might go, and why.
It could help, but it's not very likely.
The gun and shooter may not be local. The gun may have been bought, sold, traded, or stolen outside the local area or time window. What if it's somebody who used an extra Glock .40 bbl in a Glock 357? Maybe everybody in the country who sells 40 bbls for Glocks should check their records and voluntarily give the names to the local law?
Taking your gun in does not necessarily help them catch the right bad guy unless you did it and you bring your gun in, it just helps them eliminate a lot of the wrong good guys they shouldn't even be looking at in the first place w/o probable cause.
If the girls had been molested, or drugs had ben found at the scene, would every swinging Tom, Dick, and Harry in the county be asked to voluntarily spit, piss, or jerk off in a cup?
Imagine how usefull it would be to LE if eveybody underwent periodic drug testing, and everybody had blood, hair, fingerprint, and DNA samples on file!? We all did that voluntarily?
Imagine how usefull it would be if every time there is a burglary or robbery, we all volunteered to let 'em come in and look around the place, go thorough our pockets, and check our bank accounts just to be sure we don't have the loot...
So, are you going to volunteer all that info for every crime just in case? Just the serious cases? Why not?