Visual phototransduction, neurons depolarization when no light: why?
Short answer
The reason for the depolarized state of photoreceptors in the dark is unknown as far as I know. It probably has its roots deep in the evolution of the eye.  

Background
Indeed, photoreceptors are continuously active in the dark. A steady current flows through open channels (mainly Na+ ions). This current is called the dark current and it partially depolarizes the photoreceptor cell. The depolarized photoreceptor releases neurotransmitter (glutamate) to secondary neurons. Upon illumination of the photoreceptors rhodopsin molecules are isomerized to the active form and the photoreceptor cascade (Fig. 1) is initiated. This ultimately closes the cation channels in the photoreceptor's membrane, stopping the dark current.  This leads to cell membrane hyperpolarization and inhibition of glutamate release to the second-order neuron (Fig. 1).

Admittedly, I do not know why phototransduction exactly is organized this way. There is a lot known about the evolutin of phototransduction (e.g., Lamb et al., 2016), but why the dark current exists is unknown as far as I know. I surmise it is probably an evolutionary relic. Evolution eventually has to work with pre-exisiting features to generate new structures, or alter them. Simple photosensitive spots evolved into the complex eyes observed in today's vertebrates. Evolution thereby used what was there and that happened to be an energetically unfavorable 'NOT' gate.


Fig. 1. Phototransduction in photoreceptors. source: Kolb, (2012)

Reference
- Kolb, Webvision. The Organization of the Retina and Visual System (2012)
- Lamb et al., Molec Biol Evol (2016); 33(8): 2064–87