We carry a spare unmounted tire with our motor home as we have done in our previous motor homes. We have Coach net service but have never called them. Is it difficult for them to find roadside service...
I've been driving for over 50 years and can't remember ever using a spare on any vehicle I've owned. I, like you, have Coach Net and if I ever have a need, I'll wait for them to find a tire. But its good to be prepared if you have plenty of space to carry a tire.