C Major, A Minor, C Ionian, D Dorian, E Phyrgian, etc. are usually the first scales taught because they have no flats or sharps. This works especially well for piano students since one can say, "It's all the white keys on the piano" rather than confusing a beginning student by saying Bb, or something like that. I dislike the whole appraoch of teaching C Ionian, D Dorian, E Phyrgian, etc. I will explain at the bottom of my post how I like to teach modes.

As to your reference for tabs of other guitarists, and they always playing in C Major, that's just a stroke of luck that all the tabs you looked at were in C Major. I've only seen like 2 songs ever in C Major (although I've seen a million in A Minor). I do see a lot of songs in G Major, and many, many, many more in E Minor. The reason for this is that the diatonic chords for these keys are just easier to play than those of other keys. If you play a song in G Major, you could play the I, ii, IV, V, and vi chords without playing a bar-chord (G Major, A Minor, C Major, D Major, and E Minor, respectively). If you were playing in Eb Major, however, you'd have to use bar chords to play most of the diatonic chords.

People write songs within the scope of their ability, and therefore, the vast majority of songs will not be modal (since few people understand modes) and will be in a simplistic key (because surprisingly, not too many people thoroughly comprehend bar chords either).

**Modes, as Taught by TheDirt (if I were to teach)**
Rather than looking at relative modes, I would like to teach parallel modes. Teaching C Ionian, followed by D Dorian, then E Phyrgian, F Lydian, etc. the student will not understand very well. If you play a background piece with a tonal center of C, and chords following C Ionian, the student might play D Dorian and say, "I'm using D Dorian, but it sounds the same as C Ionian..." Well, that's because they are the same!! The way I would teach it is as follows. I'd teach the step pattern for the modes, then get the student to apply (write down on paper) all the modes to C. They would end up with C Ionian, C Dorian, C Phyrgian, C Lydian, C Mixolydian, C Aeolian, and C Locrian. Then I'd have the student play C Ionian over a C Ionian progression, C Dorian over a C Dorian progression, etc. This way, the student would see that it's not using different modes from one key that makes the sound different, but the step patterns in the modes that defines the mode. Playing different modes with one tonal center really brings out the sound of the modes, I think. Well, that's all well and good, but I don't teach (but I am available if anyone wants me to write lessons for their web site, like a guest column of sorts, hint hint). Oh well.
**End Rant**