If I were you, I would continue to try to find deals as time allows, and take listings when convenient for a few extra bucks.  

There are a more than a few land flippers in New Mexico - and given the language you shared from their website, I have a feeling that's the kind of seller you're dealing with (and they can be a great source of below-market deals).As for the pitfalls - it sounds like you already understand the limitations you'll be dealing with (no utilities, very remote, not near any kind of convenience).

I use them myself for business and find them convenient and price effective. 

During 2007-2011 the Euro was strong and it was convenient for Europeans to invest in the US.

So many parents come in to visit students who live in dorms/very small apartments and need a convenient place to stay. 

Other areas where I found homes that match my specifications far South East Aurora and some areas fairly far North of Denver Metro were not much better for drive distance or convenience factor. 

When it's important, you can stick to your guns (wow factor items) but otherwise there's a lot of deferring to the path of least resistance.For example:I'd like the spiral staircase to the roof deck located inside >> rejoisting roof supports, building a shed on top vs a hatch, possible bulk plane issues, taking up too much space to leave room for doors, $$$$ >> okay fine the staircase can stay outside >> team breathes a sigh of relief, I simply sighAlso, I always want to start shopping for finishes so they're ready to go when we need them - especially since I look for those special finds that aren't available on demand - but there's no convenient place to put them before we've done floors and drywall.  

Marie says above and use convenience rather than price to make your offer strong.

You can always specify a 24 hour cleaning period (or longer) between stays, which would allow you to prepare the room at your own convenience when you come home from work, school, or the like.If you would like to hire a cleaner to do the cleaning, it just comes down to managing their schedules and booking requests.

@Tony Iaconelli Assuming you have good credit, you will normally get 0 percent  convenience checks from your credit cards.