Why do neurons have a negative resting potential?
Essentially all animal cells maintain an ionic balance causing a resting potential of about -70 mV in order to maintain their internal environment including pH, ion concentrations, osmotic pressure and volume. (Lodish, Molecular Cell Biology)  Neurons developed from existing types of cells and it's unlikely that the cost of maintaining resting potential in the neuron could have driven evolution of an entire alternative system to provide the homeostasis supported by the existing system.

Note that the depolarization of the membrane at any particular place during an impulse is very short so the impact of the ion flows have only limited effect on the cell's overall internal environment beyond requiring adjustment by ion pumps for the losses involved.  It also is not obvious how the wave-like characteristic of a nerve impulse could be generated if the membrane did not carry a nonzero potential; there would be no stored energy (in the form of ion gradients) available to make the pulse swiftly spread across the membrane.

Another point to consider is that the perhaps 15% of a neuron's energy spent on replacing leaking ions may have some hidden usefulness.  This paper suggests that neurons may actually be set up to leak at a rate higher than they would if it were minimized.