That's not the case at all. A mutation is a rare occurance, and when it does happen, it tends to happen in a first-adaptor, not all at once in an entire population. That first adaptor doesn't even have a 100% chance that it will survive to breed, much less birth an offspring, and even when the offspring is born, that doesn't mean that the mutation will be passed along. For instance, the two-headed snake is unlikely to have offspring which each have two heads. Genetically engineered pigs, which carry organs for humans, are also not assured a 100% chance to produce offspring which carry those same genetic alterations.
Contrary to your claim of mutation-proliferation being "intuitively obvious," the opposite is actually the scientific reality.