Then a direct current of 100 mA will drop 50 mV along the trace. This may be acceptable for digital power and ground, but it is a substantial error. Circuits that are further out along the same trace will be subjected to the full error. Resistance decreases proportionally as you increase trace thickness and width. Ground and power are the most important connections.
Ground is usually a little more important than power.
One of the most common causes of EMI is an RF voltage on a ground run. This can be eliminated by proper grounding. While you probably cannot reduce the peak amount of power that the circuit draws, you can provide that power and keep it clean. Use heavy traces to provide both power and ground. Make sure that there is at least one electrolytic capacitor from each supply to ground.