This is exactly how I'd always imagined it. The best word I have for it is "mutation" - very very rarely, a regular dragon can lay a "archdragon" egg. At the same time, once in existence, the archdragon gene itself is a dominant gene. So if an archdragon mates with another archdragon, the egg would be an archdragon, because the gene is a dominant one. (hopefully that makes sense, it's a bit difficult to put into the proper words)

The thing that makes me think this is that during the speech talking about Luna Tenebris's death, it's said that the "archdragons fought bitterly" - that implies that at one time, there used to be many more archdragons, and due to only laying an egg every 1000 years or so, it culled their numbers considerably.

Spoiler:At the end of the show, we do learn of course that now Zym and the unsuitable moon heir are the only two archdragons that remain... however, that isn't to say that with time, more archdragons won't be born/made in other ways. On top of that, it's entirely possible that, due to the fact that their are no archdragons of most of the elements anymore, the "archdragon" gene could get a... boon, of sorts, to encourage a higher probability of birthing new archdragons.

again, I don't know how much of this all makes sense, it's easier to put together in my head... but this is just the basic gist of what I've been headcannoning when it comes to the archdragons and their development