That's different from what you're suggesting, because you're right that the crash reports are analyzed with heuristics to guess at memory corruption. Aside from the privacy implications, though, I think that would have too many false alarms. A single bit flip is usually going to be an out of bounds write, not bad RAM.
This isn't really feasible: have you looked at memory prices lately? The users can't afford to replace bad memory now.
I had memory issues with my PC build which I fixed by reducing the speed to 2800MHZ, which is much lower than its advertised speed of 5600MHZ. Actually looking back at this it might've configured its speed incorrectly in the first place, reducing it to 2800 just happened to hit a multiple of 2 of its base clock speed.