A satellite launched from near the equator will orbit near the equator. Most of the time this is what they want. However sometimes they want a satellite to orbit in high latitudes. For this they launch in the high latitudes. It also helps if the rocket goes over the ocean soon after launch. That way anything that falls down soon after launch falls into the sea and not into someone's house.
Well, the satellites launched in the US are launched from our southernmost states almost exclusively. After achievig orbit, they adjust based on mission. For example, Musk has launched over 500 communications satellites and intendes to pretty much paper the globe with them over time. They're packed into the launch vehicle in large batches, then they head for where they will stay. You undoubtedly hit on one reason for picking FL. But, there are notable exceptions. Musk doesn't launch from coasts.
I like this idea, but I don't know how well it competes with the other plans. You know about high speed trains, you put the launch vehicle on a high speed train, get it up to speed, and then maintain that speed while climbing inside a mountain tunnel, exiting going 300-400 mph, whatever we can get out of that technology.
Well, let's remember that escape velocity for Earth is ~25,000 mph. Earth's suface is moving at about 1,000 mph at the equator, so that can make a bit of a difference. You don't see many rockets launched out over the Pacific Ocean on a western track. The reason is that's counter to the way Earth spins, so one would have to make up for that. This is a HUGELY studied issue, of course. There have been ideas that are a little similar to your train idea - such as launching rockets from what would amount to a gigantic rail gun. There have been ideas such as lifting rockets with airplanes or baloons to save rocket fuel, which is a large percentage of the weight of a rocket. So far, what gets used for the larger rockets is launchig toward the east from southern states. Europe is pretty much north, so they launch a lot of their big stuff from French Guiana.