Plato gives multiple hints across his works about the esoteric, unwritten teachings [1]. We can only speculate about the content; for me, they were surely tied with the Eleusinian Mysteries [2]: early, myths-driven psychonautics based on ergot.
If we never had writing, would the Huns have carried forth Platonic wisdom? Would it really have survived thousands of years of cultural evolution and the decline of Greek civilization itself? Who even is the "we" who should consider it important?
> that would be another benefit: it would also filter unimportant works over time.
How would it even be possible to know what's been lost in the oral tradition without anyone writing things down? Only takes one autocrat to massacre followers of a specific tradition to effectively erase it. Things get filtered based on their ability to survive, which is partially a function of "importance", whatever that actually means at a given time.
> a third benefit: only people interested and caring enough would know Plato. Not dilletantes.
This just seems like unabashed elitism. A "benefit" of the oral tradition is that knowledge is reserved for the deserving? No thanks.
Tired Alfred North Whitehead quotes aside, he's basically the single most influential author in the western tradition, arguably even eclipsing the bible.