> However, you're not feeling the latency. You're noticing the presence of two distinct signals.

Not necessarily; it could be an electronic instrument.

I once tested a "e-piano -> midi -> PC -> headphones" chain. The latency was not really noticeable when I pressed only a single key, but actually playing was impossible. After I replaced a (software) component with something with lower latency, it was bearable. While I cannot precisely estimate the latency reduction, I would guess that it was less than 30ms.