TM insurance

We just bought a used 2619 TM and I was surprised when our State Farm insurance rep told us that yearly insurance for just the detached trailer would be $369 a year. I was told the trailer is insured by our car insurance as long as it is attached to the car. If we do not intend to store valuables inside the trailer when it is parked in a campground and, though we are leaving on a long cross-country trip and have never trailer camped before, we do not intend to do a lot of dry camping until our feet are good and wet with the basics.
I would very much appreciate hearing from some of you long time TM owners as to whether you think separate trailer insurance makes good financial sense and if so why?

Thanks,

Marty