It has to do with the difference between work and energy. Work = force X distance. If you drive 60 miles in one direction and then drive 60 miles in the opposite direction, mathematically you have done zero work, but we've used 120 miles worth of energy (gas).
Similarly, because the same number of electrons were moved the same distance (current) with the same force (voltage) in both directions (positive and negative), the net work is zero. That's not very helpful when you're interested in how much work we can get out of a machine, or how much heat we can get from a heater.
So, we go to RMS. It allows you to add the work done in the negative direction to the work done in the positive. It's mathematically the same as running your AC power through a rectifier and converting it to DC. You're squaring the values to make them all positive, averaging the values, and then taking the square root.
You could do the same by using the absolute values of voltage and current, but that's a nonlinear operation and doesn't allow us to use a nice equation.