Makes sense. That said, I assume that since the car is still on payments, then it's not old enough to be considered the kind of car one would immediately drop coverage on once it's paid off. Is that correct, OP?
The only place you could save some money is on deductible. My bank made me carry a $500 deductible on C&C, even though the insurer offered a $2,000 deductible. That change saved me about $140 a year in premium.
That amount of extra risk ($1,500) is well worth it, IMO, because it takes only 8 or 9 years (with compounding and a modest return) to save up for that extra deductible in the event you have an incident. Given than I've been driving for >20 years without using insurance, I'm well ahead of the "game". If you get in a major accident at least once a decade, you probably should not be driving.
It also dissuades a guy from getting costly repairs for small cosmetic damage. IMHO insurance should only be used to recover a vehicle loss, as any other use of insurance is just recouped by the insurer anyway in the form of increased premiums, etc.
Some idiot with a land yacht and lacking the skill to drive it backed into my fender on my car in a parking lot when it was 5 years old (and didn't have the integrity to stick around and take responsibility). Would have cost north of a $1,000 to get it repaired. Wasn't worth it, because I had no intention of selling the car. Still driving that car, mangled fender and all, 10 years later. And (back of the eyeball calculation) several thousand richer because of it.