The concept of human space or 'the Empire' is quite well established, so well that if we ever do travel to the stars we are likely to play this out as our destiny because it has become so firmly entrenched in our psyche. In most cases, from Asimov to Star Trek, there is one government, usually with loose control over day to day life on the planets. Using this archtype allows the author to bring in a whole universe and way of life with relatively few words.
As far as I can remember, it was Asimov who started this concept or at least made it popular. It has been expanded by dozens, if not hundreds, of others and has survived many changes in technology and politics and continued to evolve. In many early visions, the Empire or Federation was seen as a good thing, a government that was honorable, honest and just. This mirrors what we thougth of our government(s) in the 1950's. As time has gone on that government has fallen to military domination as in 'Star Wars,' corruption and hypocracy as in 'Dune', or corporate takeover as in many stories including 'Aldeb Wars.'
Which is more 'correct' is a meaningless question. Unless human nature is modified, it will take the same path as all human civilizations, it will start out honest and just, the powerful will constantly gain more power and influence until it serves only their needs. It will collapse, a dark age will set in and another civilization will rise in its wake that will immediately begin the cycle over again as in the 'Worlds Apart' series. If there is a modification to human nature, we can be sure it will not be generated by a cabal of benevolent scientists as on Kassidor, but will be invented by those working for the powerful and will be used to make humans into ants or something equally tractable. The results will be similar to Kassidor in that we will enter a more-or-less steady-state culture where history and progress will stop.
The human space concept generally does not include the alteration of human nature, meaning that we can be sure to encounter all phases of civilization at some point or another. The interesting times are when the civilization is young ('Star Trek', 'Aldeb Wars') and when it is old ('Dune', 'Foundation'). The middle years of a civilization are the right time to live in it, but not the most exciting times to write about.
The biggest problem in building a government that spans light-years is of course transportation and communication. Thru most of its history, communication has been thru something called 'sub-space radio' or something like that which is like radio but faster, and transportation has been by spaceships using warp drive to achieve faster than light travel. For a bit of recent history these technologies did not look attractive and some type of teleportation, often via worm-hole, has been used (Hyperion series, Dorrick & TongSu series, Aldeb Wars). Today there is math that once again opens the possibility of warp drive, though it requires the same singularity engeering used in wormholes. Needless to say, without faster than light transportation and communication a government or corporation spanning multiple star systems cannot work. If faster than light transportation and communication is not possible, even if we achieve interstellar travel, we will have star systems that are almost completely isolated from each other as in Allistair Reynolds 'Revelation Space' or the Gordon's Lamp series here.
Why is this concept so popular in Sci-fi? Why do we have so few stories in which there are many human planets linked with faster than light travel but politically independent? I don't believe there is something deep in human nature that will cause us to unite as soon as we achieve faster than light travel when we can't unite even when we are only hours apart by commercial jetliner. In some cases it can be postulated that we were united because of the threat, real or imagined, from some alien power. This makes sense in some stories but not in stories where there is no credible alien threat. I believe there are two reasons. One, the organization providing the interstellar transportation and communication is the uniting influence. This is seen in 'Dune', 'Hyperion', 'A Matter of Oaths' and 'Aldeb Wars'. In this model the interstellar transportation company or government functions as a government of the starlanes, but usually has very little power on the ground. Each planet is functionally independent in all matters but interstellar commerce.
The second reason I think this archtype is so popular has nothing to do with future physical or social science and everything to do with the dynamics of the publishing industry in modern times. Asimov sold well, therefore publishers were glad to get other stories like his. Authors learned that publishers liked this, and since they wanted to also get published, they used the same formula. A few of them sold well also, convincing publishers that this was something they wanted more of. Star Trek and Star Wars used this already popular concept and gave us pictures to add to the concept. We all accepted it as a valid formula. Thus it became something publishers were even more likely to favor. It is something we now all understand and feel familiar with, so much so that if we were to suddenly discover a warp drive today that could give the average settler passage to a new world for under a thousand dollars, we would probably build a unified government of human space because we have already been programmed to do so.
How realistic is such an organization? Probably not very. Given the means, people will emigrate to escape whatever oppression is bothering them at the time, corporate greed if it was to happen today. The last thing they would want to bring with them is a government of, by and for the rich and powerful. As much as we sci-fi readers have been programmed to expect a galactic empire, most real colonists will not be sci-fi readers and might not have gotten the message. The colonies will have important and powerful people, people who chafe at bending to a government light years away, and will likely declare their independence as many colonies have done from the 1700's on.
The time frame of this organization has been given as anything from 2250 or so to twenty thousand years in the future. It is my belief that our current civilization, usually known as 'Western' civilization, is entering steep decline. We are no longer politically and economically capable of putting a man on the moon, even if we still have the technology. No great projects such as interstellar expeditions can be mounted in a capitalist society because the return on investment is measured in centuries, not quarters. It is also impossible to mount great projects like this when the rich no longer contribute to society and all the funding has to come from the backs of people who cannot even afford a doctor visit. Thus I believe there is no chance that our current civilization will found the empire, federation, or whatever it is first called. Since our current civilization is a big one, it's decay is likely to take a thousand years. A new civilization takes a couple hundred years to rise, thus 3200ad. is as early as I believe it can happen. Some will say that China is becoming very active in space exploration, and it is possible, but I believe they are already too infected with the 'this quarter's bottom line' mentality, as well as a schism in society between haves and have-nots that will drag them down into the same abyss we are falling into.
But that all sidesteps the most important problem, the Fermi paradox. Interstellar travel is one of the most important things in all of science fiction, but if the laws of physics really allow it, even at a small fraction of the speed of light, why wasn't some culture a billion years older than ours here selling real estate as soon as the Earth cooled? About the only reason we can think of is that before a culture gets to the point where it can fly between the stars, it gets to the point where it has no need of planets. Without the need of planets, what form would the human empire take?