Let’s assume he was real. What’s the benefit to him that he’s remembered?

This is not a rhetorical question. Maybe some of your offspring has higher chances of survival if you’re remembered?

We only have 2 books out of around 16 from Homer, so a lot has been lost already.

Yeah, except Homer is likely ahistorical.

And the Trojan Epic Cycle contained eight epic poems. We just only have two of them. We've also lost the rest of the epic poems. We have a fraction of what was considered great even 1,200 years ago.