The reason for over/under interlacing at the crosses is that it introduces a certain amount of resiliency into the finished wheel. The spokes don't go straight from hub to rim, but instead have a bit of shallow bend on the way,

When a spoke is stressed, the bend can accommodate the load by being pulled straighter at the expense of the partner spoke, splitting the effect so neither spoke sees as much change in tension as they would if not laced. Since spokes break through metal fatigue induced through cyclic tension changes, this approach increases the long term life expectancy of a wheel.

This benefit works both in the direction of mitigating stress increases and, possibly more significantly, reducing the effects of tension reduction so that a spoke that might otherwise reach zero tension doesn't.