The next thing I'll throw out there is that there are many ways to skin a cat, and you may not be as confused as you might think.
Here's the thing... like hunter says, we're trying to memorize these patterns so we know where the notes are across the fretboard. Lets start with the major scale like you're talking about. Now, the practical end goal here (think of it as a tool that we're adding to our guitar tool belt) is to be able to see the major scale for any given key across the entire fretboard. That's the long range goal. But to get there, we use patterns to group notes that are close together.
What gets confusing is that there are different ways of explaining where these patterns are and how to visualize them across the fretboard. Many teachers use the "CAGED" system, and other methods start pattern one on the low E string, the logic being that where you start with your first note.
The Fretboard Workbook is a Musicians Institute publication, and you might be interested to know that their method works just as you suggest, with C maj scale pattern 1 starting on first fret. Check it out, its a great book and will de-mystifie all this stuff for you.
