Biometrics were a very crowded market during the 1980s and 1990s when it was a newer idea and electronics were starting to make things practical. Lots of ideas were tossed around before the industry pretty well consolidated on fingerprints with a side of iris imaging and hand geometry in some more security-sensitive niches. It mostly came down to cost: fingerprint scanners, even before the modern capacitative type, came down in price much faster than other types of imaging (visible rather than IR sensors, glass platen allowed for fixed focus, etc). The widespread use of fingerprint comparison in criminal forensics also mean that there's an older and stronger academic literature on fingerprint comparison, whereas other types of biometric sensors often involve proprietary match algorithms and you have to rely on the vendor's assertions about reliability.

Of course everything around cameras has come down in cost tremendously since then, so palm imaging is probably reasonably priced now, but it lacks a clear enough advantage over better-established methods for anyone to switch over. Besides, just the fact that you have to position your palm the way you do makes it difficult to install them in most practical door situations. Fingerprint sensors turn out to be very compact and fairly intuitive to use.

I scoured Amazon's sales materials around Amazon One very closely, because I found it fascinating that they were seemingly trying to revive the technique. I was surprised they were doing it as a payment device, but it made more sense when I found materials (I think old FCC filings) that suggested that it was originally designed as an access control product and perhaps "pivoted" to payments later. The strangest thing about it though was how unconvincing the sales materials were, it felt like they were really grasping at straws for a reason to select it over other options.

From what I could find it doesn't appear to have been an acquisition; the regulatory paperwork was all filed under some LLC but it seemed to just be a front company for Amazon which is fairly common for that kind of thing. So my best guess is that it was a pet project of someone influential enough to burn some R&D on it, and maybe pivoting to payments and putting them in Whole Foods was thought to maybe be the hail Mary that would turn it into a real business.

The actual integration with the PoS in the stores was clumsy too, they Velcro'd an NFC antenna to the side of the credit card terminal to use to make payments by proxy card. I originally got obsessed with it because I was trying to ID the suspicious device Velcro'd to the payment terminals at Whole Foods!