I believe the M3 pump is very much like the M5 pump?
The M cars do not have an integral fuel pressure regulator built into the fuel filter. They also run a much higher fuel pressure, I believe up to 70-75 PSI?
The issue with running the tank too low is risk of fuel starvation during hard corning and possibility of leaning out the fuel mixture and causing the combustion temps to quickly climb.
The M cars also have a fuel baffle right at the fuel pump pickup to help reduce fuel starvation during hard corning.
The fuel does a few things to help out the pump and injectors.
The fuel actually lubricates the fuel pump and injectors and also cools the pump and injectors.
If you starve the fuel pump too much, you risk reduced cooling and lubrication as well as putting the engine in a risky situation where the combustion temps can quickly rise and cause knocking/detonation and possible engine damage if continued to be driven hard.
I also believe the M pumps may not last as long as the non M pumps due to their increase pressure and more demanding application??
This is my point of view based more on the E39 M5 as I have had my hands on many more of them than the M3.