It appears the LASD is not just at the top of the list, but essentially is the list: they account for 93% of the violations.
Which, as you point out, is not surprising. The LASD is enough of a mess that I've heard other nearby police departments complain about them, not to mention their history of gangs, corruption, and conflicts with the Board of Supervisors and FBI.
In California it's generally the county sheriff who issues carry permits. Apparently sometime in the past few years municipal police were also given the authority to do this, but for decades I believe it was just the sheriff. And it was discretionary and highly political--urban sheriff's departments were invariably, "no", unless you were a high profile figure, whereas rural sheriff's departments were typically an easy, "yes", unless they had a reason (good or bad) not to. And sometimes there were jurisdictional fights where rural sheriff's departments would bend the rules and issue permits to residents of urban counties, (arguably) sometimes just to spite the cities. Like most jurisdictions in the US, sheriffs are an elected position, and very often crudely politicized, especially in states like California with strong urban/rural partisanship.
In any event, it's likely most Californians still go straight to the sheriff's department when seeking a permit.
Historically (as in past 100-150 years), the Deep South and West, though today probably only states like Mississippi, Alabama, Louisiana, etc. Virginia, North Carolina, and Georgia now have rural/urban divides that are stronger (more predictive) than, e.g., racial and class divides. Historically the West was rather homogenous politically, relatively speaking, but that's rapidly receding from memory. Though if you squint both Democratic and Republican West Coast politicians in some state (e.g. governor) and national offices (senator), but definitely not local offices, tend to still be a little more centrist than you'd expect as compared to their counterparts back east.
Which, as you point out, is not surprising. The LASD is enough of a mess that I've heard other nearby police departments complain about them, not to mention their history of gangs, corruption, and conflicts with the Board of Supervisors and FBI.