There is benefit to complexity. When you say "Mike and Susan went back home because he forgot his suitcase", you don't have to repeat Mike three times because the gendered pronouns carry that information, but you also know who the suitcase belongs to and who forgot it.
Pretty sure that OP is referring to noun class systems. English doesn't use one, but most other European languages do and English used to. Like German's three equivalents to English's "the": der, die, and das, which German changes depending on the noun class ("grammatical gender") of the noun in question regardless of its actual gender or whether it even has one
Zehzins example is also true for objects.
"After the cat jumped on the table with the glass and the bowl it pushed it down." Did the cat push down the glass or the bowl? In german for example it's "Nachdem die Katze auf den Tisch mit dem Glas und der Schüssel gesprungen ist, hat sie sie heruntergestoßen." (In this case the bowl) or "Nachdem die Katze auf den Tisch mit dem Glas und der Schüssel gesprungen ist, hat sie es heruntergestoßen." (In this case the glass).
Your cat example works because it shows an example that is ambiguous in English but not in German. Zezhin's example was showing something that wasn't ambiguous in English, a language with no noun class distinctions outside of referring to things by their actual gender, so there's no benefit to having more general noun classes in that example
He was showing how gendered words can resolve ambiguity in an example were this also applies in english, so that you can extrapolate to situations like the one I (or the other replies) showed.
The post above you talks about the same. In English, if you say “I see a door and a window. It is open”, it is not quite clear what “it” is. But if door is male gender and window is neutral gender, then it becomes clear that “it” refers to window in that sentence.