Invading the NCR might not be a realistic goal, but like Caesar said, he wanted to make New Vegas his Pax Romana, and where his Legion could finally settle down and finally became its own nation.
Invading the NCR could actually work, with a nice amount of luck and good strategy. The brotherhood, far less in numbers, presented a serious threat for the entire NCR, and we know that the roads aren't safe there, meaning that there are tribes or groups of raiders. In exchange for a peaceful assimilation, Caesar could use them as auxiliaries inside enemy lines, cutting support for the troops.
Then would come the one serious battle, that would decide if the Hub falls or not (and let's not forget that Caesar's forces would be far stronger, given the boomer's support and the war trophies of the Mojave, whereas the NCR would be less powerful. And they couldn't dedicate their entire forces for the Hub, considering the menace of the brotherhood, still there, and even the borders with the Shi, who could decide to take advantage of the chaos). The Hub is actually pretty close to the Mojave Outpost, and there are no cities on the path (that we know of).
If the hub falls, Kimball (or any president) could actually be forced to negociate terms of surrender. He would be in the exact same situation as France at the beginning of WWII, when the Marechal Petain did surrender. The Boneyard would be cut from the main roads. Same for Dayglow and the southern cities ; basically, the entire south side of the NCR would be cut, if the hub falls. Sure, the NCR could actually launch counter attacks, but what would be the point, now ? The Legion could retreat everywhere in the south, and actually hold entire cities hostage, like Junktown. If pushed away from the Hub, they could retaliate by razing the Boneyard. They could force the conflict to go for years, while indoctrinating children on the occupied lands, while the NCR would be short on cash, short on morale and short on new recruits. Unless the Shi decide to support them in their times of need, the NCR citizen would not have the morale to keep on fighting.
Caesar would not have enough leverage to actually turn the NCR into the Legion, sure... but at this point, he doesn't need to. So there would come his hegelian dialectics : a compromise. Some sort of vassal state, next to the first real state of the Legion, which would change the two factions radically.
He would probably demilitarize the NCR to protect his own borders, and turn the NCR army into a police but guarantee safe commercial exchanges. Make them pay the war costs to make sure they cannot get up, until they view the Legion as a decent neighboor/master, and forget its atrocities. They could then negociate shared governance on the future NCR colonies, which would insure that they are not too humiliated, and would accept most cultural changes.
Basically, what happened between Rome and Egypt, or France and Germany.
How would there be no freedom under Mr. House? No justice, alright I get that. But,
Of course, there would be freedom. Hell, there is "some kind" of freedom in the Legion's lands, too. It's just not the main thematic of House's faction, it's not what characterizes it in the narrative.
There would be limited freedom, as there would be in his benevolent, libertarian dictatorship (if that makes any sense). Sure, come and do whatever you like, but don't ever cross the house that always wins like Benny did. Don't ever try anything against him. Don't even think about it, because his robot army is patrolling the streets, making sure this scenario cannot happen. Don't ever try to run discuss his orders, because he knows better than anyone alive.
In the NCR, at least, you have the freedom of expressing open disagreement with the main power, like most soldiers you run across do. While it's a feodal state, it's not a dictatorship per se. They cannot guarantee justice or prosperity, but they can guarantee your individual freedom.
Caesar could guarantee your security, and justice for anyone who would try to disturb your peace.
House couldn't guarantee any of this, but he could make sure that as long as you trust his wisdom, you will win. Money, properties, women, no problem. "It's the old vegas all over again, baby."