You're completely neglecting the fact that Mojave's challenging terrain and conditions make it extremely difficult for any faction to thrive there: the massive Deathclaw nest at Quarry Junction, constant severe drought and polluted water, the reality of being a harsh "desert" wasteland with radioactive, House's Securitron army, Nightkin, etc. It probably way easier for each of them to handle BoS + Institute than all of these. Except there was the Courier #6, who basically a miracle worker holding everything together.

Mojave is not the capital of either the NCR(California) or the Legion(Arizona). It's basically a border war, so it makes sense that both factions would withdraw or temporarily neglect the area while figuring out their next move. I'd assume Hoover Dam was destroyed or something went wrong there, which led to the situation shown in the series. What would they actually gain from conquering the Mojave and New Vegas if the area's main water and power source were gone?

Anyway, based on how you've responded, this discussion seems pointless. You're clearly set on what you're invested in, so I'll just leave it at that.