This is one of the things that makes me hesitate when someone asks me to teach them piano. My experience has been that music theory is really easy to learn, it is just a system like any other. If you can pass a demanding college class, you can likely teach yourself music theory within a few weeks. And that is what I did, all the way up to functional harmony.

When teaching students, however, I'm always worried that I would be going too fast. Because my go-to is to teach the way I would have liked to have been taught, which would be something like the following:

Here's middle C. Observe the groupings of two and three black notes. You count up and down by letters to get you D, E, etc. (30 seconds)
Now, the black keys are flat/sharp corresponding to whether they are just above or just below a certain note. (30 seconds)
Observe the symmetry of the keyboard. Each octave is identical. See the pattern from C to C (2 black keys + 3 black keys). This repeats across the keyboard. (1 minute)
Now, each key is equidistant in terms of pitch from the next (semitone), black/white keys included. Each octave is twice the frequency of the previous octave. This is in terms of ratio (so the ratio would be the twelfth root of 2). Regardless, what you need to keep in mind is that starting on a key is the same as starting on a different key in terms of the ratios of the pitches, and that's why music when transposed sounds "the same". (1 minute)
Now, look at middle C. Here's a C major scale (demonstrates). As follows from the previous point, every other major scale would be the same sequence of distances of whole notes and half notes, by symmetry. We will start from C major for illustration purposes. Think of the notes as 1, 2 ... 7, 1. The basic diatonic chords are the first, third and fifth note starting from a given scale degree. (3 minutes)
A typical chord progression would be I IV V. From the previous point, you know what those chords mean. Melodies tend to use the notes in the chords, but the exact specifics of chord tones/non chord tones are better left for later. (4 minutes)
Try your best to memorize all of the major scales by next week.

So, that's a total of about 10 minutes of teaching.

It all seems perfectly logical in my mind. What would go wrong with this approach? I find that when I explain it to people, they can be too polite to let me know if it's all going over their head.