Is it possible to achieve a "happy ending" for everyone?
No. This is the greatest strength of the main storyline - it forces you to make trade offs and assess what your greatest value is - stability? Freedom? Democracy? Technology? Personal wealth?
It also lets you come up with a nuanced answer to this question - one could support any of the major factions, or independence, and justify it by appealing to any of the above values. It makes you question what those words actually mean: Which faction really offers the most stability? The most freedom? What really constitutes freedom anyway? Is the NCR truly a democracy? Will Mr. House actually be able to accomplish his goals, and will doing so actually improve the lives of the average wastelander? Could the Legion possibly transition into a more open, tolerant society once it settles down? From which faction do I stand the most to gain from, on a personal level? Different players and their characters are going to answer these questions differently.
I've roleplayed all kinds of characters, taking very different paths - among them, a sadistic NCR patriot with Very Evil karma, an amoral mercenary working for the Legion, a starry eyed tech scavenger who sided with Mr. House, and a bumbling idiot who wound up destroying every faction and blowing up Hoover Dam itself through sheer dumb luck, leaving only Vegas itself intact. For each of these playthroughs, I imagined how these characters would justify their decisions.
In my own opinion, the best option is for Independent Vegas, with self-policing robots. The Legion would be vanquished (ideally with Caesar dead), the NCR bruised and humiliated (Oliver, Kimball and Hanlon left alive), and the smaller factions either negotiated with peacefully (the Followers, the Khans, the Kings, the Three Families) or put out of their misery (the BoS, the Fiends).
This is far from utopia - without a centralized power structure, the ambient level of chaos, uncertainty, and violence remains high. But in my opinion this is better than cementing the power of a totalitarian empire (Legion), a corrupt oligarchy with a thin veneer of democracy (NCR), or a grandiose, delusional autocrat (House). It's better to ensure that nobody has power, rather than giving it to those who will only abuse it and oppress others. Perhaps in time, a real society can coalesce in the Mojave, and since I've eradicated the most violent gangs, I think there's a better chance of that happening.
Of course, the interesting thing about Independence is that it could really go any number of ways. The vision I outlined above is just one possible version of independence; for example, you could argue that as long as the Dam is standing, some up and coming power is always going to want to invade Vegas, and so the best way to ensure long term peace is to destroy it, along with the Securitrons...but of course this will also greatly set back the potential level of development in the region.
You could also view "independence" as actually meaning that the Courier becomes the sole ruler of Vegas, and depending on what kind of character you are, maybe he/she is even worse than any of the other factions. One my favorite playthroughs was as a hardened criminal who hated the NCR; he sided with the Legion up until the very end when he turned the tables on them and used the Securitrons to take over everything, becoming a warlord who rules Vegas with an iron fist. He had successfully managed to ensure the deaths of both Kimball and Caesar, leaving the two largest factions without leaders.
