Evidence that matrix multiplication can be done in quadratic time?

It is widely conjectured that $\omega$, the optimal exponent for matrix multiplication, is in fact equal to 2. My question is simple: What reasons do we have for believing that $\omega = 2$? I'm aware of fast algorithms like Coppersmith-Winograd, but I don't know why these might be considered evidence for $\omega = 2$. Naively, it seems to me like a classic example where a community just hopes that a result is true purely for aesthetic reasons. I would love to know if that's essentially the case here.