Well, it may be ancient, but the medieval image is also a staple. I heard somewhere that unicorns were associated with Christ, so they needed to be caught by a virgin. It's interesting how people perceived and understood Christianity.
In general, it's a cool thing – incorporating pagan beliefs into Christianity. There's Cerberus there, it seems he guards the circle of gluttony.
Oh, I didn't mention bicorns, but I still think it's a meme – the word "bicorn" doesn't really hint that it's a horse; you could call a goat and a cow that too.
I repeat that unicorns were more often depicted as deer, bulls, and goats, not horses.
And, in my opinion, Greek myths are boring. But a unicorn is a dangerous monster – the question is, why is it needed? What makes it better than hydras and wyverns that serve evil factions? Nothing, it's the good nature that makes the unicorn close to elves and fairies.
I like the brutal and terrifying unicorn more than the cute pony, the pet of fairies and girls.