After reading a bit more about this here (thanks for all the informative replies) and on colour management in general, I'm pretty sure I prefer my monitor being able to display all 256 different intensities of one colour even if they're not exactly the same as some standard colour, than a scaled and truncated fraction of those (which seems like it'd just cause more visible banding.) The example image shows that clearly. I adjust my monitor's contrast and brightness to my preference, and colour perception is quite subjective anyway (not to mention affected by viewing conditions, hence those hooded monitors and controlled lighting when it is important) so I think colour management is not for me.

In fact, I'd say that if you displayed that example image simultaneously on a non-colour-managed sRGB monitor (logo visible), colour-managed sRGB monitor (logo invisible), and (colour-managed?) P3 monitor (logo visible), no average user is going to want the middle option.