Speaking from personal experience, I'd say the fascination with splinter states stems from the desire to see not just a new country, but a new culture emerge. That culture will then influence the cultures of its neighbors, either by example or by opposition. Sovereignty has a way of making a state define itself as a distinct entity from its neighbors with distinct values. It's one thing to shift the course of events in a nation with which we're all familiar and alter the national character. To imagine a state that never had the chance to exist offers, in theory, greater flexibility and creativity in defining the national character, and I think that's a tantalizing prospect for the lovers of allohistory. Some countries and cultures prove more plausible than others. That's why we get glimpses of Texas, Pernambuco, a thousand New Englands and "Cottolvania." It's not within my powers to imagine how a Republic of the Rio Grande could possibly succeed under the historical circumstances with which I'm familiar, but in the right hands, I'm sure it'd be quite interesting.
Even an implausible treatment of a sovereign state offers us something, and it's not just entertainment. I love allohistory because it strengthens my understanding of our own history. Allohistory is, in part, the study of plausibility and inevitability, an analysis of how things came to be, how unlikely our present world is, and the myriad possibilities we could live in. Even a bad allohistory deepens that understanding, and perhaps inspires a better writer to pen something more plausible and enticing. To quote the great charlatan Thomas Edison, "Through all the years of experimenting and research, I never once made a discovery. I start where the last man left off. … All my work was deductive, and the results I achieved were those of invention pure and simple. ... I would construct a theory and work on its lines until I found it was untenable. Then it would be discarded at once and another theory evolved. This was the only possible way for me to work out the problem. … I speak without exaggeration when I say that I have constructed 3,000 different theories in connection with the electric light, each one of them reasonable and apparently likely to be true. Yet only in two cases did my experiments prove the truth of my theory."
