I think the most likely good faith version of this is that the LACSD wants to prevent people that are bad actors from obtaining the licenses. Where this touche

I think the most likely good faith version of this is that the LACSD wants to prevent people that are bad actors from obtaining the licenses. Where this touches on abuse are people who are not convicted of any particular criminal offense related to firearms, or people that have had negative contact with the LACSD. So on the "positive" side this might allow them to prevent a person who they strongly believe is a gang leader but has not been convicted of any offense from obtaining a permit. On the "negative" side this might be people like defense attorneys, anti-police activists, or private investigators who have a tendencious relationship with the police from obtaining such a permit. Or in some cases maybe even people who have simply had a negative interaction -- filing reports critical of officers, etc., who are being spitefully targetted. The law attempts to strike a balance between the concerns and law enforcement overreach and exists for a reason.