I actually liked the core concept of the Legion. While their methods are draconian to say the least they are still crude but effective. Using heavy military discipline with the total war and scorched earth concept- I could see that forging together a wide spectrum of different tribes, severing their former tribal links and replacing it with allegiance to the Legion.
So a game set in Arizona post Caesar would actually be pretty interesting. Like it was mentioned before: a civil war between different generals? Maybe even during the invasion of NCR after the victorious Hoover Dam battle?
Although I have to admit that certain elements badly need revision and were not well thought out. Here is a couple:
Medical service: relying on healing powder and deliberately suppressing more advanced techniques is just moronic, because the only real thing you achieve is a high hemorrhage of your own units, amongst them experienced and well co-working units, which in turn will amplify your own losses when the "old guard" is replaced with new inexperienced personal that need time and practice until they fit in with the unit. This also has a severe effect on morale when you know, that even the simplest cut can resort in death (infection) because your own army lacks basic medical service. Not to mention that anyone with even the slightest wounds probably will get left behind because they will be dead anyway. There is a reason the most effective armies of the real world enforce the slogan "No man gets left behind!".
Uniform: bright red in the desert? Not to mention against anything resembling green? I get the roman theme but when you are facing enemies who extensively use firearms then that is just presenting yourself like in a shooting gallery. It worked in real life ye olden days because most of the heavy fighting was melee range.
Tactics: ONLY relying on melee for the bulk of the Legion is not a good idea. What happens when people without guns go against people with guns? Yeah. If it were up to me then I would use the front lines as hybrids who are trained and equipped with basic firearms and melee weapons while the rear lines would be equipped with more heavy hitters (machine-gunners, sharpshooters, grenade launchers etc) with melee for self-defence. During contact the rear lines would suppress the enemy fire with accurate and deadly fire while the front lines would immediately engage and close the distance using typical cover fire tactics. Once the distance is closed they would engage in melee fighting for the shock and awe effect. Since the NCR seems to be primarily composed of conscripts with only basic firearm and single fighter training then this would most certainly conclude in complete chaos and unnaturally high casualties (anyone caught in melee fighting against trained adversaries will most likely be killed on the spot or at least severely maimed), completely demoralizing the enemy in the process. While this is going on the Legion rear lines could provide cover for the first lines, suppressing any NCR reinforcements/counter-attacks. Of course since the game itself will probably use Beth's Gamebyro tech then this would remain a general description device with it being reflected in how the legionnaires are equipped and divided into units. Trying to create any organized fighting in that is like trying to organize drunk football fans at a stadium: no matter what you do it will resort into a all out brawl.
Of course there are several aspects that I would like to see fleshed out when it comes to the military side of the Legion but those listed here are by far the main bugbears I had with them in FNV. In conclusion to give general sense in comparison the other factions of the Fallout universe: while the Brotherhood/Enclave type organization would rely on small numbers with extremely advanced tech to compensate their inherent flaws (shutting out new recruits) and the NCR would rely on a mass of individually badly prepared but low cost units to simply "swarm" their enemies then the Legion, while laking in both the high tech of the BOS and numbers of NCR, would be known for their tactical and operative prowess with a strong officers corps, traditions and well-trained/disciplined units, using brutal and aggressive (yet effective) warfare to throw their enemies off balance (in short: what actually helped the real Roman Legions become so successful). IMHO if used properly then this would give a much more believable faction then it is currently.