While all cases I'm aware of are highly supernatural in some sense, most omnifertile beings I've heard of cannot change form at will, and almost never on the scale of minute details. Most are also considerably less knowledgeable than would be expected to have conscious control over minutiae like reproductive compatibility, so that doesn't seem likely at all.
The notion that their elemental/alignment-infused nature acts as some sort of glue or blank slate might work, but isn't specified or required.
That said, the OP's conclusions depend on a couple assumptions.
The first is that half-X creatures are indeed objectively superior to mundane ones, which is likely untrue. Things like maturation time, dietary requirements, and other traits beyond a stat block can have a massive impact on the creature outside the dungeon- their odds of getting the food and care they need to wind up as an elite adventurer rather than a malnourished bandit, for instance. Otherwise, you would expect the most successful races to be those that were the most powerful- like dragons, celestials, and fiends, obviously, but at the very least trolls or somesuch.
Since all the world's greatest legends don't concern said creatures (or at least, not them winning), and indeed since mortal races still exist at all, rather than having been shoved aside by stronger beings, it can probably be inferred that powerful creatures often have limiting factors that prevent them from steamrolling anything else they come across. Given that information, there doesn't seem to be any reason a half-fiend or dragon-touched would be immune to those principles either, and would likely find their unique gifts rather less impressive than at first glance.
Secondly, it makes the critically flawed assumption that being good for the individual is good for the species. Even if a half-celestial were considerably superior to its peers, it might be too self-sacrificing to breed especially well, for instance. As mentioned earlier, dietary and environmental needs, length of reproductive cycle, and other such factors can make an otherwise imposing race (dragons, for instance) not especially successful as a species. The "if that were true the whole world would be dragons by now" principle is arguably even more true here.
Third, it makes the assumption that severe dilutions are at least as strong as pure samples; again, this isn't necessarily the case. Aside from whatever bizarre and not especially rational results having a hint of fiend blood might have, there's more logical issues that might come to the fore. Someone with a pinch of dragon blood might have hoarding tendencies beyond what's strictly productive, for instance, without having any advantages to pull it off well or compensate for it.
Short Version: There's no reason to assume it'd be that ubiquitous while being that faint; either the whole world would be dragons (or half-fiends, if hybrids have some critical advantage over their stronger parents), or there's some reason why it doesn't work that way.