"Now all the myriad American ancestors think they're descended from nobility and are entitled to display that English family's crest."
In England, you're not talking about a "crest," you're talking about a coat of arms, which were awarded to specific individuals, not families. A firstborn son could apply to the College of Arms on the basis of his father having borne a coat of arms, but the coat of arms, if granted, would be "differenced" with the addition of some small detail, such as a stripe or a border. That's why very early coats of arms are exceedingly simple, and late ones are complicated. Very, very few US citizens are entitled to apply to the College of Arms for their own, differenced coat of arms, as a result. But, a very large majority of US citizens actually do have some relation to nobility, usually through second and younger sons striking out for the colonies, in hopes of making their fortune, since they were not entitled to inherit under primogeniture laws.
I misstated something: I should have said a a very large majority of US citizens with early colonial ancestors have some relation to English nobility, for the reasons mentioned.
Thank you, I'm actually armigerous on my father's side, so I'm familiar with the details of heraldry.