I have often wondered if I had started guitar in my teens instead of my early elementary years, would I have wanted to simply play chords? And is it possible to "learn" guitar through chords?
Chords are not basic, but they are an element of instruments that can play multiple notes at once. They are used in most songs, and everyone wants to learn just enough to play around the campfire.
Most people do get bored eventually, and this causes most to put down the guitar...
I think that chords can be used to teach just as much, if not more, than a method book using single note songs.
Let's start at the basics.
A chord is minimum a 3 note event that happens. This event can be played using many different rhythms. Once a student finds out they can play a few chords, why not change the rhythm to incorporate multiple strum patterns. Suddenly the student is making his or her own song. in-between two chords a student can arpeggiate the chord, and suddenly the student is learning the string numbering/naming system as well, and potentially finger picking.
Once students have a good grasp on a decent number of chords you can talk about improvisation. What key are we in, what chords sound good, and what is a key.The student is now learning basic/advanced theory.
And finally, the student may want to start working on writing or creating solo's... and now we can begin with single note songs in order to teach the student where to find the notes in the key they are playing in.
In my opinion, it all depends on what the goal of the student taking lessons is... but for the most part students want to learn songs to impress their friends. Starting with chords is a great way to do this, and slowly lead them into learning melodic lines to help them create either a solo, learn a solo, or keep them going with a new challenge.