Formality used to be very important in language in less egalitarian societies, so it's really an artefact. I have seen it argued that (in German at least) gender can help native speakers with word recognition - i.e. it's easier to differentiate die Brücke and der Bruder with the articles than without.
But it's interesting to speculate on what English does which could be considered pointless:
* Gendered pronouns (he/she/it) - some languages e.g. Persian/Farsi do with a single pronoun for both.
* Number agreement for 3rd person verbs - i.e. he goes but they go.
* The continuous aspect. In many languages the expressions 'I run' and 'I am running' are identical.
* Articles. 'A cat sat on the mat.' Many languages do without these words and rely on context.
* Required tense marking. 'I speak', 'I will speak', 'I have spoken'. Some languages make the distinction optional - i.e. 'I speak' can mean 'Today I speak', 'Tomorrow I speak', 'Yesterday I speak'.
Or things which could be useful to introduce to English:
* Animate/Inanimate pronouns - i.e. a formal distinction between 'it' (used for objects) and singular-'they' (used for humans and similar).
* An actual second-person plural - like y'all, yous, etc. rather than 'You' functioning as both singular and plural.
* A distinction between we (including the person to whom you are speaking) and we (excluding that person). 'We are going to the zoo tomorrow' - does that mean me and you, or me and my family?
* A grammatically distinct future form - 'I walk' -> 'I have walked' in the past tense, changing walk to walked, but 'I will walk' in the future using the same form as the present.
My point is that, in English, it's possible to leave someone's gender entirely unstated, whereas in Spanish someone is either "el amigo" or "la amiga" with no other options.
Also, if you don't know Spanish, I'm not going to teach it to you.
This is one of those things that's both true and false at the same time.
It's true it goes back to 1300, but it had also fallen out off fashion and was considered "wrong" later on. Languages change, and don't do so in a linear straight-forward way. From our perspective, it's very much a neologism (although it's been a few decades, and arguably already passed the neologism stage).
I don't know, the sentence "by 2020 most style guides accepted the singular they as a personal pronoun" doesn't scream "it's been used like this for centuries" to me.
To me, it doesn't matter much, because there isn't much "extra" to learn. The gender is derived from the word suffix, and there are three or four rules to that, so it's both extremely easy to learn and to apply to unknown words.
This is unlike, say, German, where each word has a random gender and you need to learn it along with the word. There, I agree, that's unnecessary overhead.