I'm skeptical even this wouldn't have vulnerabilities however, as history has shown us that cryptography which has not been formally proven is often broken.
[1] I'm using the word "sound" here to differentiate the noise in the auditory sense from noise in the "signal versus noise" sense.
[2] https://en.wikipedia.org/wiki/Block_cipher_mode_of_operation...
Again, I have no proof of concept here, so take with a grain of salt.
E.g. use something like a illuminated disco ball that continuously randomly changes the source light angle and intensity.
Something like, a vibrating module that you don't really notice but which clouds out any sounds the microphone would pick up (or, to go your route, injects fake audio). You turn it on when you want to be sure the microphone isn't listening, just like you can cover the webcam.
[0] https://www.amazon.com/Mic-Lock-Microphone-Blocker-Pack-Surv...