In a way, filming in color is like creating a topographic map. One where the hills and valleys of the map represent different color values from the scene that you're filming. This map is created by your cameras hardware.
For decades camera makers (and before them analog film manufacturers like Kodak or Fuji) have been working to make cameras more sensitive to light, able to record in lower and lower amounts of available light. There are various reasons for this, like potentially lowering the costs for movie productions because less light means renting fewer lighting units, less time spent setting them up and less electricity used to run them.
There are various ways of making cameras more sensitive to light and each brand makes their own recipe by trading off different factors like photosite size, higher gain circuits (and the noise reduction that can sometimes be necessary) and (the one factor that all manufacturers seem to agree on using) lowering color sensitivity.
Lowering the color sensitivity of a camera allows more light to be recorded by each photosite on the camera sensor, BUT also limits the amount of unique individual color values the camera can record. The camera can no longer "see" pure saturated colors, delicate secondary colors or true blacks and whites.
In our topographic map analogy this would be like making a map that only records small hills and valleys where there should be mountains and ravines!
Camera manufacturers try to stretch the smaller, limited color signal that was recorded to fill out the full map (re-mapping) using software like in-camera color profiles or LUTs.
Stretching the signal out ends up leaving the color looking thin, flat and if the color saturation gets turned up too high - garish, with unrealistic skin tones and broad stretches of flat, featureless color.
Just as leaving values out of our topographic map robs us of the dimensions of the terrain, leaving color values out of our images robs the dimensionality of our films.
This is just one of the reasons why three-strip Technicolor can't be recreated digitally. Cameras just don't record enough information to fill out Technicolor's "map". You can play with colors in a grading session all you want, but you can't remap color values your camera couldn't see in the first place.
Thankfully Optical Radiance's analog color for digital cinema tools and system are now here to fix this (and other) problems!