The advantages are huge, but they are mostly technical and boring. In sort, the visual quality and realism is vastly increased with little performance impact. Textures, lighting, and frame buffers all benefit from the use of linear space. http://http.developer.nvidia.com/GPUGems3/gpugems3_ch24.html
For materials, if you want good values for creating something realistic, look at PBR charts.
It can get messy and confusing, but it would be even more confusing of the engine worked in or had an sRGB mode.