why do we rearrange them for a scale
Because a scale is all about playing notes in order of pitch. (Of course your diagram is also arranged in pitch order, but it doesn't contain all the notes in the full C major scale including all the repetitions within each octave.)
A scale is not about putting notes in order of importance - it's simply about laying them out so that from any given note, you can easily find where the other ones close to it are. In that sense, it is related to laying out the instrument so it's easy to play - it would probably be unintuitive to have a piano where the notes pitches jumped about rather than steadily increasing as you moved from left to right.
why do we ... put them in "order" to create a Major chord
I guess we typically say that a major chord is 'C E G', in that order, for similar reasons - because that's the order you see the notes on the keyboard.
You might notice, though that the major chord is (in a sense) a re-ordering of the notes according to the harmonic series, as it contains the notes C, E, and G - the first three that occur in your harmonic series.
How come we dont use the early overtones in order from a Harmonic series to create chords/scales?
There are lots of different scales and modes, and most of them do use some of the notes corresponding to the early overtones. But having notes corresponding to early overtones isn't the only criteria for a useful scale - we want to come up with a set of notes whose pitches create interesting harmonies and tensions with each other, not just with the overtone frequencies in the tonic (root) note.