One of the main reasons there aren't any comps in New Mexico are because of a lack of delegates. There are zero in the state, so that means we have to rely on Colorado and Arizona delegates to host competitions. That becomes difficult for getting reliable venues that won't pull out suddenly, because communication is limited with little to no in person contact. Even with a few competitors trying to host a competition, it remains difficult to find a venue as they aren't sure of the risk.
The other main reason, is there is a lack of community. There are 32 entire cubers in the state for 3x3, granted there are definitely more who have no idea of CubingUSA that aren't registered there. But the number isn't drastically more to warrant much development of a community. Other states have dedicated cubing clubs at colleges and schools because of their higher numbers of cubers, which NM simply doesn't have.
Yet another side reason, is location. New Mexico's most populated cities are pretty far from any other major cities. Albuquerque is a solid 7 hours away from both Denver and Phoenix, which means there won't be a lot of out of state competitors. This even further relates to the second reason, because there isn't a large community in state, they have to make up more of the price from out of state competitors, which is difficult to guarantee as historically NM comps get very few competitors in general, half of which are from out of state. So it's just difficult to guarantee any sort of profit or even just breaking even with NM comps.
This is hopefully changing though, as there has been some talk at some NM colleges of trying to host more competitions, though this is still difficult because of the first reason. There are pretty much only three competitors across the entire state who compete at more than just NM comps. That is me, where I live in Farmington which is pretty much as northwest as it gets, so I'm equally far away from the 3 closest cities to regularly host competitions, that being Phoenix, Denver, and Salt Lake City. The second is Estevan Lujan, who is more southern somewhere around Santa Fe to Las Cruces region. So it's difficult for him to travel to many comps, especially due to high college work loads. So he mainly goes to Phoenix or Denver comps if he can manage. And the final cuber is Caleb Dye, though I'm not exactly sure what region he comes from, I can assume it's around Albuquerque as that's the most populated. But he can similarly also only manage Phoenix and Denver competitions.
Personally, as one of the fastest in the state, I have learned that with no community and no delegates, it becomes nearly impossible to host competitions consistently like the surrounding states can. I'm hoping Estevan can work together with the few cubers around NMSU to start hosting more competitions, as he was talking with them at the latest Albuquerque competition a few months ago. But we can't be certain of anything as NM cubing is still much younger than almost any other region in the US.
If you think you have the capability, there is always the option of getting in touch with the delegates from Colorado or Arizona to host more competitions. You can work with them to find out what you would need to host a competition, and they can try to help with the process as much as possible. It's not an amazing option and it requires a bit more effort from both sides, but it's a way to make competitions more likely in New Mexico.
I would also love to have more competitions that are less than 8 hours away, but I'm not currently in a position where I can realistically work to organise a competition, and Farmington is not really a great location for a competition, being 3 hours away from Albuquerque, 4 hours from Santa Fe, and even more from anywhere else in or out of state.
If you have any other questions or clarification, I would be more than happy to help out, being one of the few active NM cubers, and the only active one on the forums.