Unfortunately this approach makes you quite unique for fingerprinting
As opposed to sharing your actual latitude,longitude and microphone readings?
It doesn't have to be random to be a problem.
In general any sort of intervention that moves you away from Joe average is bad news for fingerprinting.
More sophistication in this context often makes things worse not better. e.g. In this context volunteering info on every request (fake or random doesn't matter) certainly makes you unique, because the average user doesn't do that
The draconian rhetoric you are using is the same logic someone uses to advocate for no symmetric encryption because it can be implemented incorrectly.
Reiterating your basic fact about fingerprinting doesn't change this, or negate the rest of my statements you ignore because you think nuance and user requirements can be reduced to a binary.