Still, in an environment as populated by firearms as the fallout universe, it makes no sense to base your entire fighting force on melee, giving firearms just to the people who can scavenge them.
Now I wouldn't mind it if the legion simply used more varied and more primitive firearms (pipe rifles, single shotguns, pistols etc.), but ditching firearms entirely? No wonder they are having trouble conquering the NCR.
I'm not sure what games you played, but in my playthroughs the Legion definitely used guns, even for the low recruits. Could have been part of the mods though, I guess.
Oh, in-game they do use guns quite often (AFAIK in vanilla, higher ranks use them more often than recruits but mods usually just give everyone guns) and in-game even the melee legionarres can easily swarm you and murderate you. It's part of the game, because melee and long-range options must be made at least semi-equal so the player can go either way (though who'd use the melee option in a game with such horrendous FOV is beyond me).
I really didn't mind the slavery, the authoritarian approach or the misogyny (okay, maybe not that last one), but as far as I recall, Rome was not entirely populated by luddites.
Neither is the Legion, really. Caesar just favours low-tech weapons that soldiers themselves can maintain and/or create, so they don't have to rely on centralized equipment/management structure to sustain themselves. It's for practical reasons, mostly, and part of the guerilla style campaign that is the reason the NCR is so overstretched from defending against.
Sensible enough, but shaping the doctrine in such a way that encourages scavenging weapons would get equal or even better results. Better than focusing the combat doctrine on melee formations easily countered by automatic (or even semi-automatic) weaponry, at least.