I went from repairing building amps in my spare time, to now doing this for a living.
Before I started working on amps commercially I only worked on/ built gear I was interested in myself, mainly vintage valve amps.
Once I started fixing gear on a commercial basis, which I did several years before it became a full time job, I had to learn how a much wider spectrum of gear works, eg effects pedals, which I have very little interest in as a user, although I found the electronics very interesting and stimulating.
If you are going from the transition of doing some lessons on the side, to doing it as a full time job (as I have), then you will be subject to market forces, and you will need to decide whether you can afford to turn away prospective students who want to learn something you don't feel you can teach them, regardless of whether you think they "need" to know this or not. I don't refuse to fix chorus pedals because I think chorus is a hideous effect.
I suspect that there are few guitar teachers who can teach all styles (for example could you teach Danny Gatton's picking style?), and I'm sure all teachers have their specialist areas.
Nevertheless, I think some understanding of theory is a good idea as it can provide a framework for some students to understand what they are trying to achieve. Remember we all learn at different rates and with different methods.
Of course in an ideal world we would all learn everything by ear, however not everyone has the talent to do this (I certainly don't), so some theoretical support is of benefit. You should bear in mind that the OP is clearly a very capable guitarist, and I suspect few of his prospective students will achieve that level of capability.
I have a reasonable grasp of theory, and have never found it particularly troublesome to get my head around (although I am mystified by any guitarist's obsession with modes.......).
As an example, I think you should be able to teach a student how to work out the notes in a chord, and thus work out the chord shapes and arpeggios, eg a Dmin9, or an G13.
I think the bottom line is that you need to feel you are giving value for money, which incidentally I feel I do with my repair business.