Nope. I have the same full coverage as my other vehicles. (I haven’t tested just how “full” it is, though.)
Insurers use actuarial tables and byzantine math to calculate your premiums. Possibly their magic chart just shows that my make/model/year is low risk. For grins some time, get an insurance quote on a Dodge Ram (assuming you don’t already have a Ram) and a Silverado or Sierra of the same year. I’ll bet you a penny the quote you get on your Ram will be significantly higher. Despite it functionally being the same vehicle to you and me, to an insurer the Ram is the one statistically more likely to be owned by a drunk driver and/or a moron.
It’s the same thing with my FZ6R. That bike has a detuned R6 engine in it and gets from 0-60 exactly as fast as an R6, but its insurance premium is like a quarter as much. But more dudebros buy and crash R6’s, and only silly old men carefully ride FZ6R’s. Or something.