Resurrecting a slightly older thread here, but some musings on Legion territory:
Firstly, it seems that when you stop to read over it all it's likely that Caesar's claim over "all" of New Mexico is likely a bluff (or perhaps just misunderstanding/disregard of strict borders as is to be expected in a Wasteland without westphalian ideas) as in much as his control over Utah is. Considering that Denver is marked by Lanius and Ulysses as being effectively the Legion's most eastern frontier, parallel to the Mojave as it's most western and both equally difficult to besiege.
I'd say a good rule of thumb for the Legion's easternly border is probably Interstate 25 at the Colorado/New Mexico border. This would especially make sense with their pre-established capturing/interaction with the Midwestern Brotherhood based out at Cheynne mountain. Though, if the Legion managed to overcome then during their Denver campaign and it was supposed to be their main HQ, I imagine the Midwest BoS is in a very dire state indeed. Or never was in a good one, depending on how they actually exist in the canon.
Secondly, though this is more speculative than my last point. Caesar's claims may not be bluffs at all, but what he considers control/claim is just fundamentally different to what our assumptions are. Namely, he likely isn't at all thinking about map borders beyond easy reference for region naming. His claims could be more-so fixated on the power balance in the respective regions, i.e how unchallenged his "influence" or claim is. Even if the Legion doesn't literally stretch to the border of Kansas within New Mexico, if the Legion has absorbed or destroyed basically all of the main or relevant societies within the state, and the rest is barren Wasteland, then the state is his. Compare it to say, the Fallout 1 world map (i.e picture hypothetical New Mexico wasteland maps in a similar fashion), if Caesar is coming from the southwest, and sieges Boneyard, Hub, Brotherhood and Necropolis. Does it matter if his territory literally reaches Mariposa, Vault 15 or the Glow? Not really, no. The region is his. But in the technical sense, the Legion's most eastern point would be Necropolis.
This actually gives more credence to his approach in Colorado and Utah. "Much of the Utah" is his because he's disintegrated various tribes there already, destroyed the state's most powerful and basically only point of civilization and has a highly populated, well armed nomadic raider-tribe under his beck and call. Are there any Legion stationed at the Great Salt Lake? No. But it doesn't matter, because his influence/power within the state is dominant and growing, though he can't claim it completely as there are still large pockets of competition/resistance (surviving New Canaanites, Sorrows, Dead Horses etc) and the same is likely true of Colorado. I'd imagine his ease of access also plays a part, he claims less of Colorado because navigating and squeezing resources is a logistical nightmare.
My third point connects to my second, in that I think people underestimate the savagery/primitive state of the Four Corner Wasteland, and how they haven't as been as developmentally lucky as the Mojave or California. We are given flavour of this in Honest Hearts, where Utah is very much painted as a completely primitive state. New Canaan is the only place safe/worth trading with, and the region is otherwise inhabited by outright spear-chucking tribals, nomadic primitive raider-tribes or stationary warlords with "Gas-station forts". I.e in Utah without New Canaanites, your highest standard of civilization is basically equivalent to Motor-Runner or Driver Nephi. Raul and Caesar both imply that Arizona, and by extension the rest of the Legion's territory is very much the same way. Pockets of civilization surrounded by a majority population of tribalistic nomads.
Thus to my mind, the Legion has effectively pulled a more rape-y katamari damacy on the entirety of the societies within the comparatively barren Four-Corners Wasteland and in that way their claims are both legitimate whilst also the Legion itself still maintains its role as a purely nomadic army that takes its entire rolling momentum wherever it goes. As Dale Barton shows, pockets of subservient civilization exist within these territories but they are minimal and were always the absolute minority compared to the majority tribal population (which is now absorbed entirely into the Legion) of the Four Corner states. Which is why the Mojave and the West are so critical/important to the Legion: Not only will it represent a fundamental change in the structure of the Legion, but the vastly more civilized and connected lands of the Mojave and California will force the Legion to adopt entirely new methodss and ways of running their territory/claims. Arizona is likely a crucible of Legion millitary power/control and likely has numerous camps/war-settlements feeding into the Mojave, but Legion territorial claim is all about the power and influence rather than literal borders, trade routes and stationed garrisons as with the NCR.