Your example does not work at all for me, I hear nothing. Please make a simpler example with just playing audio if the audio is the problem, since I can't easily tell if one of the other events or a third party addon is causing a problem.
And just to get a clear answer.
Why does C2 not support pitch change?
Construct 2's Audio object does not implement an audio engine. It just lets you use what the browser provides, and if the browser does not provide pitch change, the Audio object cannot have it either. You should be aware "playback rate" does not necessarily mean pitch change - it can also mean playing the sound in a sort of slow-motion effect, without affecting the pitch. Different browsers implement playback rate differently so it's not guaranteed you'll get either effect unfortunately.