You might not hear it often, but that doesn't mean it's barely used. English is spoken by more than just English people. I reckon I hear "score" used in the sense of twenty of something than I hear words you'd probably describe as more common, such as "laden" or "bereft."
I live in the southeastern United States. It's common for conveying the size of a group, for instance. If a lot of people showed up to an event but not on the scale of hundreds, it's common to hear "scores of people."
It's not common in my job to talk about scores as a metric because 20 isn't a natural unit for my work product, but I wouldn't be surprised to hear it like that, either. We still use "dozen" and "gross" for other non-decimal groupings much more commonly, e.g. "a dozen doughnuts."
As someone who has lived in the west and northeast, I’ve never heard the word score used to mean 20 outside of Lincoln’s address. In most dialects in the US, scores has just been relegated to another synonym for many and doesn’t get used outside of it’s plural form. Interesting to hear that there are places that still use it occasionally, much like I occasionally hear “gross” used as you mention.
