At the risk of drawing attention to the elephant in the room, unless information is now using the transporter, computers "transfer" information by copying it and erasing it from where it was previously. It's possible computer technology works completely differently in the 24th century but, technically, the Doctor is being erased and copied everytime he's moved to a mobile emitter.
Again, it's backward to start from first principles and then claim that the situation onscreen "should" conform to them. The facts onscreen are as they are. We have to accept that and work in the other direction to find an explanation that justifies it.
If the EMH were the same kind of computer program we use today, then it would follow that he could be easily copied ad infinitum. But he isn't. With the exception of "Living Witness," he's been consistently portrayed as a unique entity that is removed from one location when transferred to another. And that doesn't fit the kind of computer programs and data we use today, but it does fit quantum information. So it makes sense if the EMH is based on quantum computing, which is distinctly different from the kind of computers we use.
Anyway, I've always felt that trying to use our modern browsers and word processors and games as an analogy for a conscious, thinking artilect is as nonsensical as trying to use a houseplant as an analogy for a human mind. They may be of a broadly similar category of being, but they're very, very far from interchangeable.
My rationale for this is basically the better travel times get, the more free-flow of information occurs, and the more cultural uniformity occurs across the universe--the smaller the universe gets.
I don't think that follows at all. If anything, the free flow of information that the Internet has allowed has resulted in the opposite of cultural uniformity, because once-isolated fringe ideas are now able to get broader hearings and larger followings. And historically, the parts of the world where different ideas have been free to mix and cross-pollinate, far from being melting pots that merged into homogeneity, have instead been the birthplaces of multiple new, competing philosophies and religions, as the different ideas have mixed and matched and clashed and reacted in a variety of different ways. When people have that many possible paths to choose from, there's no way in hell they're all going to mutually agree to head in the same direction. Cultural uniformity is only found in isolated areas where exposure to new ideas is limited.
The Federation eventually covering the entire galaxy just seems to be a natural result of the fact that once there is "you can cross X amount of space instantly" you'd need a regulatory body to handle questions of soveignty, planetary rights, appeals, and so on.
Circular argument. They'd need a central body because they'd need a central body. You're only assuming that such a need exists, and that's the very assumption I'm challenging. Yes, of course there would need to be regulation, but again, you're completely failing to grasp the sheer scale of the galaxy. There is simply no way that a single bureaucracy could handle millions of worlds, let along billions. You'd need a bunch of smaller, more local bureaucracies.
The idea that a system needs a central authority at all is somewhat old-fashioned. We now understand that in many cases, local-rules organization is more effective. Look at the Internet. Decades ago, everyone assumed that the future of computers would be a single vast central mainframe that stored all knowledge and answered everyone's questions. Instead we've got a huge number of local servers, a decentralized, distributed network.
Don't get me wrong -- I'm anything but a libertarian. I believe there needs to be central government on some scale to maintain law and ethics and safety. But there has to be a balance. The larger the number of citizens or states that a central government has to manage, the less efficiently or responsibly it can serve and protect them. On a larger scale, you'd need an alliance of distinct governments, and on a larger scale an alliance of alliances, and so on. Ideally there'd be a set of basic ethical principles that they'd all agree to abide by, and international conventions for interaction and diplomacy and cross-cultural law, but there couldn't effectively be a single central body administering it all. Okay, maybe some kind of post-Singularity superintelligence could have the attention and processing power necessary to manage that many entities at once, but would we really want to be governed by a higher order of mind whose decisions we're not intelligent enough to fathom, let alone have veto power over? If we want a democratic system, a system where individuals have any rights and responsibility to shape policy, then there has to be a practical limit on how much territory that particular system covers. Representative democracy is a middle ground between centralized and distributed decision-making, and it's dangerous to let the balance shift too far in the centralized direction (although the same goes for shifting too far the other way, because that way lies anarchy).
If everyone also agrees on X principles, is it more likely the universe will be six different "Federation of Kronos, Federation of Gorn, Federation of Romulus" or one gigantic Federation?
Neither. For one thing, you'll never get everyone to agree on everything, nor should you. Even if certain fundamentals are agreed upon, there are always going to be differences in interpretation and application. And as long as people have the right to think for themselves, there are going to be a lot of things they never agree on. The idea of a single, homogeneous culture spreading across the galaxy is hideously dystopian. As long as people are diverse -- and an interstellar, multispecies population would be orders of magnitude more diverse than we can comprehend -- they need to be given options. The only way they can all be free and represented is if they have a variety of different societies to affiliate with. Any universals would have to be very broad, adaptable sets of standards that the different societies are free to apply and administer in the ways that work best for them.