What do you mean by harmony in this case? Because my personal experience was that BECMI's various editions created market confusion between itself and AD&D for its entire existence.
For example, my first gaming group in 1980 was using the AD&D 1e core books. I ran out to buy them and stopped cold at seeing how expensive they were to my 10 year-old's $2.00 per week allowance. The Player's Handbook and Monster Manual were each $12.00, and it was a whopping $15.00 for the Dungeon Master's Guide, and then there were the other books, too. I picked up the Red Basic D&D boxed set, thinking it was the introductory version of AD&D. It did advertise itself as a complete game, which looked like a much better deal than the array of more expensive hardbacks. Oh, how mistaken I was.
I'm sure new entrants into the D&D RPG market today are probably confused about 4.0 versus PF, much less understanding pre-1e (Classic, Original, or whatever we'll call it), 1e, BECMI's various incarnations, 2e, 3.0, and 3.5.
I was twelve when I started playing and wasn't confused. D&D and AD&D had different names. I figured, and rightly so, that D&D was an easier version of the same game, and it didn't bother me that the rules were different. I just figured BECMI was targeted toward beginners. I rather liked BECMI, and played it quite a bit with friends, only getting into AD&D with 2nd edition, though I collected the 1E books. I didn't think it was confusing, but perhaps it was to many others, I really don't know.
When I said "harmony", I was partially referring to my personal experience with both rulesets in part, but mostly I was referring to the fact that TSR continued to publish products for both rules sets for quite a while.
They had different names, but both had Dungeons and Dragons in the name. They were different flavors of D&D, not just because of campaign worlds, but because of the rulesets. BECMI appealed to all sorts of people who wanted a simpler, faster system, not just kids. Heck, I loved that it scaled to 36th level and Immortal level play, even though I never got a campaign that far. The BECMI Rules Cyclopedia was a fantastic book with everything you needed to play in one nice hardback, something I wish WotC would do someday. Mystara had its faults, but it turned out to be a well developed campaign world.
Meanwhile TSR continued to develop AD&D. BECMI rulesets started in 1977 with the D&D Basic Boxed Set and finished with the Dungeons and Dragons Rules Cyclopedia in 1991. AD&D started in 1978. and supported with books like Unearthed Arcana in 1985, until AD&D 2nd edition in 1989. The editions coexisted for 14 years. Hells bells I was 12 when I started playing BECMI, and I was playing both BECMI and AD&D 2E in different campaigns at the age of 20. That longevity and the proliferation of products for both lines is what I call harmony.
When looking up the dates in wikipedia, since I am getting old and starting to forget the hazy details of the 80's, I came across this amusing quote:
Dungeons & Dragons - Wikipedia, the free encyclopedia
Unfortunately, almost from its inception, differences of design philosophy caused this dual marketing approach to go awry. Gygax, who wrote the advanced game, wanted an expansive game with rulings on any conceivable situation which might come up during play. J. Eric Holmes, the editor of the basic game, preferred a lighter tone with more room for personal improvisation. As a result, the basic game included many rules and concepts which contradicted comparable ones in the advanced game. Confusing matters further, the original D&D boxed set remained in publication until 1979, since it remained a healthy seller for TSR.
I find this amusing because it reflects the opinions of many that it is "unfortunate" whenever there is more than one officially supported edition of D&D. It is criticized as confusing and the marketing approach as "awry". However, the concluding sentence reflects otherwise. If it was so confusing, and awry, why was BECMI such a healthy seller for TSR?
Folks don't like the player base being split. They want one official, best version of D&D. Maybe if TSR hadn't published BECMI and stuck with just AD&D, the hobby would have been better off. But I doubt it. That's what they started doing in 1991, and they went bankrupt in 1997.
Above all, folks, especially DMs, want to play the game that they like. BECMI wouldn't go away for 14 years because people were still buying it, and people bought it while AD&D 1E was busy becoming a classic. If TSR had updated BECMI as well into a 2nd edition, maybe things would have turned out different for them in the 90's, maybe not; I doubt that alone would have made a difference, but some extra income could have helped.
3E didn't go away; people were still buying it, even though it was called Pathfinder and supported by a different company. WotC could have continued to support that market, and chose not to make that money. At the time I felt they were doing the right thing, now I'm sure they didn't.
People who want D&D to be only one officially supported edition have a point. It's nice to all sit at the same table and play the same game. When you invite players, it's nice when everyone knows the rules, and talks the same lingo. It's even nicer when the version you happen to like is the one that is officially supported.
People who want to play D&D a particular way other than you have a point too. It's nice to play the version of the game that you love, whether it's without miniatures, with simpler faster combat, Vancian magic, or more or less simulation/realism/wargaming/dungeon-based/encounter-based/etc and you probably don't really care what the table next to you is playing, much less what the rest of the hobby likes.
I should point out that I'm not really in favor of WotC supporting BECMI, 1E, 2E and 3.5E RAW at this time; I think those ships have sailed, in part because I don't think the staff at WotC would be interested in doing such a thing, and designers have to be excited about what they're writing about. But I do think that WotC could benefit from multiple versions of D&D that are designed to support the type of gameplay that people miss from those versions, as well as a cleaned up version of 4E that continues to cater to that crowd. (Without significant errata please!)
I'll be the first to admit that D&D is not spaghetti sauce, no analogy is perfect, but to summarize my point, I'll abuse the analogy one final time:
If you like your spaghetti sauce spicy and no one makes it that way, you won't eat spaghetti sauce (or you'll make your own). If you like D&D played a certain way, and no one publishes a rules set that supports your playstyle, you won't be buying D&D.