Earlier quoted context omitted.
TIL in some states they do emissions checks (although in a lot of states motorcycles are totally exempt from those anyway). And no, they don't do safety inspections of "specially constructed vehicles". And based on the ones I've seen, I can't imagine a world in which they'd pass. [1] [1] http://bosshoss.com/supersport-bike/
However, at least some states (probably most) require a minimum level of insurance from a carrier licensed in the state. There's nothing that requires those carriers to provide insurance to vehicles that don't meet their minimum requirements.
Don't most have a bond alternative to insurance?