You are totally right, if all I wanted to do was figure out how many total rows there were, and needed to do this often, it would make much more sense to store that number in a separate table. Unfortunately, those particular queries were just simple examples illustrating the problem --- the real program actually needed to read and use the real data. :-)
That's a good question, and one I'm not entirely sure about. My guess is that the index itself is also scattered across the disk, since it gets added to at the same time as the rows get added. So in the real query, where we are reading actual data, and not just counting the number of rows, there are actually two seek costs --- seeking to finding the correct part of the index to read, and then seeking to find the row it points to.