Wow, sorry to hear this was your experience, original poster. But I gotta say: who judges a state's bicycling friendliness by riding the interstate shoulder from one side to the other? That's plumb insane, as my Pappy would say.
I just spent 5 days covering over 300 miles in southwestern NM and a tiny bit of southeastern AZ. Silver City, Hatch, Gila, Three Way, etc. and I can't tell you what a wonderful place it was. Perfectly maintained wide roads, almost all of which had wide well-maintained bike/emergency lanes, which we didn't even use because the regular car lanes were so deserted. Perfect November weather in the low-seventies, endless blue skies, friendly drivers and friendly restauranteurs, abundant and easily located stealth camping sites. What's not to love.
Not trying to argue, but I hope nobody reads this thread and crosses NM off their list because the interstates aren't particularly fun to ride.