@txstatebass, thanks for the kind words. We're all doing the best we can with what we've got, where we are. My resume and 50 cents will get me on the subway.
I like to give some history when teaching these things, which these days are just to private students, e.g., to explain how _different_ music practice and performance was at the time the modes were in use and how, e.g., people quite often flatted the B in Lydian mode, etc., what's loosely referred to as "musica ficta" which makes a good Google for anyone unfamiliar with the expression.
What you're calling the old-fashioned way might, you're right, be a good enough explanation for a classical theory class, but it really doesn't at all address the way these thing sound, or gets used, in 2017.
@jtlessons, we're all in agreement with you for the most part - I don't find breaking the modes down into their individual intervals useful. My approach is that roots of the tree of Western music in all its forms is best thought of as the major scale, and everything else in relation to that so, e.g., I couldn't tell you the pattern of intervals in anything but a major scale off the top of my head.
This being an Internet forum, let me add something else that may or may not be related and will probably p#$% off someone - some people learn that a major triad is a major third then a minor third: C to E and E to G, respectively. This is true enough, but I don't think of it this way and I don't teach it this way. I teach it as based on the intervals C to E and C to G - the relationship of all the chord tones to the root. For me, everything relates to the root of the chord and that entire nomenclature comes from the major scale of the root of the chord, so the whole distance between components isn't something I've found relevant or useful to teach.
-S-