I find that most teachers seem to be disorganized and teach things randomly instead of building a logical program where one fundamental leads to another
I found that to be true of most teachers I've had as well, so I resolved to be different when I started teaching. I keep notebooks with a page for each student, and I record what I showed them at each lesson, and any comments on problems. Before the next lesson, a glance at the page tells me what we've done, and I can keep things orderly.
As far as leading from one fundamental to another, I agree in principle, but I'd change your method a bit. You're showing all the letter name chords before they start playing songs... the chords F and B are more difficult than the others; I start showing songs as soon as I've taught two chords. C/G7 or G/D7 is enough to get started with a simple tune, and it keeps students interested and motivated. I start with basic major and seventh chords, but I add some basic minor chords (Em, Am, Dm) before getting into F and B. It lets them play a wide variety of music before fingerings get more difficult.
I also start with the minor pentatonic in teaching lead, but I add the techniques - slides, bends, vibrato, hammer - after they've done a bit with the basic notes. Again, get some accomplishment under the belt before making things more complex.
Two things you haven't touched on are reading and theory... I start sight reading as early as possible, usually at the first or second lesson. Reading is a skill not enough guitarists have, and you have to begin with the basics. A beginner will tolerate repetitions of 'Twinkle Twinkle Little Star", but a guitarist who's been playing for a while won't - and therefore won't develop reading abilities nearly as well.
The start of theory should be the names of the notes. I start with the open string names, which are always part of lesson 1 for a beginner. After that, I add notes along with reading. The space between letter name notes is confusing for a beginner, so I show them a piano keyboard, and talk about the names coming from black and white keys. By the time they've learned the first position notes, we're ready to tackle scale theory with some background, and it makes later concepts easier to grasp.
A teacher has to do more than just show technical details, like how to fret a chord. You've also got to motivate, encourage, and help solve problems in a positive manner. Some of that comes with time and experience... but you've got to connect playing the guitar with having fun, which means making music. Start learning a song right away, even if it's only the first chord or two of a song... that helps them connect the dots between the technique of fingering and the fun of being a musician.