Low speed traction is definitely an issue in the M3. That is the trade off for a more dynamic car while in motion. However, with PSS in stock size, I am only limited really in 1st gear, and slightly in second.
You have to learn how to drive the M3. Don't jab the throttle. Be more progressive in how you depress the accelerator and you won't have as many issues.
If you want a similar car that you can hammer mindlessly, get an RS4 or RS5. That is the AWD advantage. However, the steering will feel less responsive and the car just won't feel as nimble and "wired to your nervous system" as the M3.
Precision tool: 2011 BMW ///M3
Sledgehammer: 2014 Audi S6