NM is a low population state, so there are really no TV rights to market to a new conference. I think it was go independent, drop levels of play, or drop football. (They've had football a long time, believe it or not) If you don't even have a weakish conference to try to win, it's hard to see how you build that program up. They've got the route of big payouts to come play SEC schools in the last two years, but I bet the budget they've got is pretty tiny.
If I'm Dewayne Walker, I've gone 10-40 in 4 years in New Mexico, and the local Sams Club offers me a job wearing a hair net serving up food samples in the frozen food section, I'm outta there.
That is hands down the worst scenario I've seen in college coaching, for a HC to leave this far into the offseason for a position gig. They're homeless right now - NMSU - and the Sun Belt will likely turn them and Idaho away.