It seems a bit weird that everyone would have to go to London to get to Scotland. After all, for quite a few kids it would certainly be closer to go directly to Hogwarts from their homes or possibly to catch the train at some point along the route. Why do they all go to London?
There are a couple of possible answers to this. First of all, London is where Diagon Alley is, and all the kids will have to go there to get their supplies anyway. Since they have to go to Diagon Alley, it makes sense that they go from there to the station. Even the kids who come from Ireland—Seamus, for example—would need to come to London anyhow.
There is an even better answer, however. Why do all the kids have to go to King’s Cross? Because that’s where the train leaves from. Think about it. We Muggles think about distances between places in different ways than wizards do. They can use the Floo Network, after all, which makes anywhere with a connected fireplace as close as the next room. Consider the Knight Bus. It didn’t travel by any route that we Muggles would choose. It almost seemed to be moving alphabetically, and in so doing it jumps all over Britain in the blink of an eye. So why go to King’s Cross? Because that’s where they need to be. Distance doesn’t matter.
But then, why take a train at all? That’s a whole different question. The platform and the train represent a doorway out of a world where their parents live more or less side by side with Muggles, the world where secrecy is of primary concern. It is also the world of their youth, their childhood. The doorway leads to a world where secrecy is not a problem, where they are free to learn and grow and become what they are born to be: wizards. The world they enter is not connected in any tangible way to the world of their parents. They are expected to act responsibly, make decisions about everything from bedtime to eating meals. This world doesn’t even really connected to the world of Muggles. Even the calendar seems to be adjusted, since the first day of classes is always a Monday.