It's legal in Montana, but whether it avoids taxes and other complications if you live and keep the RV in another state depends on a bunch of things, all of which depend on that "other state". For example, most states require that vehicles present in that state be rigistered and titled there if in-state more than xx days.
The insurance insures the vehicle & its owners for liability (damage to others) and for damage to the vehicle (collision and comp). If the owner of the vehicle is the LLC, then that is who buys the insurance and gets protected by it. Presumably YOU would be the owner of that LLC, of course.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL