That doesn’t ring entirely true to me, in part for the reasons @lostaccount cites. There are other elements to this, though.
I do think there’s a club/branding effect, wherein HYPS like being seen as being in their own category, and would consider moving to ED as representing a step down in prestige. Princeton wants to be grouped with Harvard, not Cornell, or Penn, or Columbia.
Second, it suits this group of highly comparable tippy-top universities to have an early round that requires applicants to signal a first choice among them. HYPS could all fill their classes many times over with superstars, and when they give an offer that’s turned down, it’s quite likely that it’s because the person chose another school in the group. Viewed that way, it’s entirely logical for Yale to want to know with a high degree of certainty that if they give this particular superstar an offer, she’s going to take it and not hold out for Princeton or Harvard. Unrestricted EA wouldn’t accomplish this.
This goes to why these schools care about yield - it’s not so much because they view it as a measure of prestige, because they’re already considered to be at or near the top. It’s more that, if they could, they would handpick every member of the class to get the exact population they want. With 70->80% yields, they’re actually not that far off, and are in the fortunate position of being able to be much more granular about who they admit. They won’t be satisfied until they get to 100% yield, though - but primarily for this reason, not because of the perceived prestige of a high yield.
Regarding EA, as far as I can tell, the only schools that use it (without an ED option) are ones that have some clearly differentiating qualities and therefore dominate a niche market. MIT and Caltech are the top science-focused universities in the country, and a large number of STEM superstars will always rank them first. Georgetown is arguably the top Catholic university in the country and the best university of any kind in DC. And so on…