The Trouble with Log
The key problem is that few cameras actually work this way. Sensors are not ideal and everyone wants pictures which look subjectively nice, which is a matter of opinion, subject, and photographic intent. Real world log profiles usually give us an approximation of log, modified by the manufacturer to achieve some goal. Generally, each f-stop's worth of information occupies roughly the same range, but this can break down at the extremes of light and dark, and variations may be offered with the intention of supporting a particular photographic intent, in the same way as a Canon DSLR's picture styles.
When the output from such a camera is displayed, we must know how the picture has been treated so that we can undo that treatment and display it correctly. Because of all this variability, monitoring equipment must have specific knowledge of the camera's luminance handling behaviour. Using the wrong anti-log curve can produce images with crushed or floating blacks, noise, clipped or dulled highlights, or almost any other imaginable problem, causing a cinematographer to make misguided decisions about lighting and exposure. With cameras generally capable of using different curves at the touch of a button, and with post-production software offering even more flexibility, it's easy for serious problems to arise.
The underlying issue is a lack of standardisation. Taking calibration into account, any viewing situation currently needs to take into account three or four different things (the camera's log curve, any creative curve, any calibration, and then the monitor's anti-log curve), and that's true on set and throughout post, representing a risk of, at best, inaccuracy, and, at worst, critical picture quality issues. Nobody's proposing a return to the days of ITU Recommendation BT.709 – a standard closer to linear than log – but normalisation is long overdue. The counterargument is that all cameras are different and attempts to force them into a single specification would risk compromise, but the existence of previous standards – such as 709, and the picture styles available on Canon DSLRs with their selection of sRGB or Adobe RGB output – suggests that it's workable for manufacturers to offer distinctive and useful options within a standardised framework.
I'm ready to be convinced that every camera system needs its own custom setup, and I stand ready to retract all of this in that case. Until that point, I shall hope that in a few years we'll be looking back on the current situation and chuckling at how poorly organised everything used to be.