Think this out a little bit. The wrist strap is there to tap off static you've built up through your clothing, shoe interaction with carpet, etc.
In a scenario where you grab hold of a 220V cable and are safely grounded through nothing but that wrist strap, if we were to assume that your body magically had zero resistance, then 0.00022 Amp would flow through that 1M Ohm resistor to ground (i=E/r or 220V/1,000,000 Ohms) saving you from heart fibrillation. It is of high resistance because that prevents you from seeing a high current flow at lines voltage but presents a ready path to ground for static.
That 1M Ohm resistor would be dissipating 0.0484 Watt if it were to bridge a 220 mains by itself (P=E*i or 0.00022A*220V), so the day one burns out is the day that Ohm's law has collapsed into the dust or that you were really unlucky and met up with something in the kV range.
Moral of the story, Wrist straps are there to prevent you from zapping silicon. System grounds are there to protect you from having hot chassis conditions that cause you to become the ground circuit. Shields, covers and interlocks are there to prevent you from sticking your hands into mains voltages which could zap you and kill you if your wrist strap was some piece of cheap junk that didn't have a proper high resistance, low wattage resistor in it.
One of our avionics shop routines is to check all new wrist straps for proper resistance (quality check that they're made properly) and all used ones to make sure the conductor path didn't break.