I don’t think that follows, that’s just the fascist argument, which is the power is an end in and of itself, and that more power in one person or one place is always better for everyone, somehow (the how is never well-explained).
History does not support this idea at all. Particularly outside actual wartime - and no, the eternal skirmishes of the wasteland are most assuredly not war (indeed most small-scale wars aren’t wars for this purpose, only total war, really). The only other time it has value is in the face of an existential crisis, but it’s a coin flip there as to whether the people/person with the power take the crisis seriously. If they don’t, it’s far worse than other systems.
This is even clear from the ending slide for Mr House, in which he shows no interest in the region other than brutal domination of his specific area (i.e. the titular New Vegas, but not the land around it, save where necessary to maintain New Vegas), and continuation of his extremely specific regime (which is a crude and wholly artificial re-creation of a pre-war situation). There’s no particular sign he’s interested in building up New Vegas beyond that, or improving the lives of people in the area, or making the area safer or more wealthy, except as in potentially safe for people traveling there to gamble (which isn’t even really gambling, in a sense, it’s more like a sort of ritual). And his level of power means no-one else will be able to improve the area either. He’ll slaughter anyone who gets in his way, and just maintain a grim, inhuman status quo.
I feel like your NCR argument is missing the point, because it almost doesn’t matter what their specific ideology is, just that it’s one that promotes a decent amount of freedom of thought and behaviour, whilst allowing some kind of societal structure (as anarchy will always turn into warlordism, 100% of the time, as human history shows) which has actual conflict resolution and so on. Yeah there will be some significant injustice, though I’m not sure I really by that there is more “extremism” under the NCR than, well, anyone else. The level of injustice, however, will utterly pale when compared to the other options.
On top of that, the NCR is the only one which allows for much potential of eventually becoming something else which isn’t just a failed state or warlordism in the longer-term. The NCR could potentially evolve into almost any kind of reasonable society, as it allows for speech, potentially allows for change (even if in part by flawed and compromised democratic mechanisms), and understands compromise. Let’s look at the others:
The Legion - They may get more powerful, and might even conquer part of America. The majority of humanity in the area (women, slaves, etc.) will suffer brutally under them. They’re not really like the Roman Empire, because they have a much stronger and more specific ideology (rather than a weighty but largely un-examined set of traditions and an aesthetic), and are totally unwilling to accept anything but total domination. As such they’re more akin to Japan in the 1930s, except even worse. There’s no way this ends well for anyone involved. The game suggests there’s “civilization”, but it’s not going actually be civilization as we know it, because it’s so ideologically-based it would be incapable of change. Best case scenario is for a Legion takeover that Caesar or the player then gets killed and then no-one has a lot of power, and some sort of council is formed that might potentially allow for change. Seems more likely to revert to warlordism though.
Mr House - He secures New Vegas and anything he needs to make New Vegas successful and defensible. Then he spends the rest of time until someone extremely powerful arrives attempting to re-create certain aspects (but only certain ones) of pre-war Vegas, and dealing with anyone who gets in his way or who wants anything different. The only good thing is he probably doesn’t go on a conquering spree, but people are probably going to have to “work around” him. He’s not a “strong leader” or whatever - he’s not a leader at all. There’s no “centre of power”. There’s just a brutal theme park. In history, there’s no benefit to “strong leaders” or “centres of power” unless they’re building something or protecting people, and he isn’t really interested in either. It’s potentially eternal purgatory. Better than the hell of the Legion, but also likely extremely stable so incapable of improving. The best case scenario would be if House decided to spread power out to human followers, and then died. But he’s not going to do either of those things, and if he died without having established a pretty solid human government and so on, he’d simply be leaving a massive power vacuum, and the robots probably couldn’t defend the place (and people probably could figure out how to take over), so that would not be great.
Independent - Pretty simple one - it’s just a matter of time until someone’s power snowballs, and you’ve got a warlord, and probably other people are also snowballing, so you’ve likely got a number of warlords, who will probably end up destroying even more, killing even more people, and leaving things even worse off.
NCR - Vegas becomes part of an existing, stable civilization, albeit one which is married to “old-fashioned” (but like 2000 years less “old-fashioned” than any of the other candidates) values. In particular they stress personal liberty and the rule of law. The former is the only way you’re going to see any change, because if people can’t speak out and so on, if they’re punished for that, as they would be in 1 & 2, you can’t really have change other than collapse. The latter is the only way things can improve long-term. Indeed, if they are problems with the laws, the rule of law actually allows them to potentially be fixed. It also has a strong interest in protecting its citizens, and improving their lives. It’s the only one which is going to build up infrastructure for people in a serious way (the Legion ain’t the Romans, or they’d have a very different approach - infrastructure first was generally the Roman way, but we see zero sign that the Legion even has competent engineers, let alone all the people needed to build a civilization), and it’ll do it with the minimum damage to existing people and probably future people.