The explanation of why there this kind of gamma mapping was introduced in the first place is inaccurate. An often cited explanation is the nonlinear sensual response of human vision; if you wanted to accurately model that you'd need a logarithmic mapping. The true reason for the need of gamma correction is the nonlinear behaviour of certain kinds of image sensors and display devices. CRT displays, be the very physics they are based on have an inherent nonlinearity that's approximated by a gamma=2.2. When LCDs got introduced they of course were made to approximate the behaviour of CRT displays, so that you could substitute them without further ado.

Another important aspect to consider is, that using just gamma is not the most efficient way to distribute the bits. You want a logarithmic mapping for that; which also has the nice side effect, that a power law gamma value ends up as a constant scaling factor to the logarithmic values.

Now, it's also important to understand that these days the bread-and-butter colorspace is sRGB and that complicates things. sRGB has the somewhat inconvenient property that for the lower range of values its actually _linear_ and only after a certain threshold it continues (differentiable) with a power law curve. That's kind of annoying, because with that you no longer can remap logarithmically. And of course converting from and to sRGB can be a bit annoying because of that threshold value; you certainly can no longer write it as a convenient one-liner in a GPU shader for example. That's why modern OpenGL profiles also have special sRGB framebuffer and image formats and reading from and writing to them will perform the right linearization-mapping.

However either way what the explanation for gamma is, the important takeaway is, that to properly do image processing the values have to be converted into a linear color space for things to work nicely. Ideally a linear contact color space.