I find the whole “semantically singular, grammatically plural they” thing fascinating because it brings into European languages (granted, English is a pretty unusual one) an idea that I previously only encountered during a brief foray into Japanese:
Most of the time, either the number of the noun is clear from context or you are completely fine not knowing what it is.
“They are waiting at the door for you.” Is there one of them? Is there more? Who cares, the sentence covers both!
Granted, Japanese has syntactic gadgets that enable you to add that information in a natural way in cases where you actually do care, but it’s still surprising at first how much communication works without obsessively marking every noun for number. How do Japanese, Chinese, and Korean speakers communicate without grammatical number? The same way Russian speakers communicate without grammatical definiteness, or English speakers communicate without grammatical perfectiveness, or all of them communicate without grammatical clusivity, etc.: either they mark it explicitly or—in most cases—they can perfectly well do without. It’s technically ambiguous, but only in the way every other word that isn’t marked for every grammatical category found across human languages (i.e. every single word) is ambiguous.
(In case you were wondering why speakers of Slavic languages sometimes tend to overuse “some” and “this” in English, that’s why: those are the way their native languages, lacking obligatory articles, mark nouns for definiteness when it actually matters; the overuse is what happens when you teach articles as “these weird formal words you have to use according to these weird formal rules” without telling your students that they actually bear meaning.)