The police union hates it, of course.
I live across the bay in Oakland, where we've just laid off 80 officers and the official police department policy is that they will not send anyone out to take a report for a non-violent crime. You go online and fill out your own police report, which I'm sure the department routes to /dev/null at their earliest opportunity.
To me civilian investigators seem like a huge net win-- they allow the police department to function more efficiently and provide better service at the same time. The objections, which mostly seem to have to do with the investigators testifying in court, seem pretty weak to me. The sort of investigative work that happens on these calls seems routine, and there's no reason you couldn't train a civilian investigator to do that part of the job just as well as the police academy does.