The scene only consists of a red texture mapped on a plane. No compositing enabled. Filmic color management with basic settings is enabled. Rendered with Cycles. No matter what color I set in the world, the red stays desaturated. Even in the material preview its not accurate. Why is that?
Also with emission shader instead of principled it looks different.
The red your colour combination is describing is the correct intention when rendered. The square is the incorrect result when considered in a physically plausible rendering scenario. Specifically, it is "correct" at only one possible intensity, which has no real bearing in a scene referred physically plausible rendering scenario.
A quick and simple test of this concept would be to keep increasing the emission of your original colour. You'll find that it skews to become a purely saturated REC.709 colour if you sample the output values, as opposed to the original intended colour ratio.
Principled shaders use, among many of the options, albedo values that represent the amount of reflection of a given channel for each of the default REC.709 three lights. It is also mixed in with other complex algorithms to yield the result. EG: The roughness / glossiness / fresnel is reflecting some of the source light itself, or other environment things.
With an emission, it is a little trickier. Your value is projected directly out. At risk of repeating some of the other answers on this site:
You cannot represent a colour that is both saturated and intense.
We are bound by the limits of the display. If we think about a heavily saturated REC.709 red such as [0.1 0.000000001, 0.0000003] we can see that we will "run out of room to express that colour" very quickly. Eventually the red channel will hit the maximum of the REC.709 display, and at that point, we can no longer "hold" the original colour intention.
So what you are looking at when you turn colour management off or use an inappropriate camera rendering transform is objectively wrong in all cases; *it simply isn't the colour represented by the original set of REC.709 ratios. Calling it "desaturated" is also a bit of a misnomer; it is a different colour entirely, and one that is based off of the original intention of the REC.709 colour triplets.
Andrew Price did a very good demonstration of this complexity in one of his videos. It is worth focusing on to begin to grasp the differences between a display referred imaging application and a scene referred rendering scenario.
In the comment above you mentioned that you are using Filmic color management. This is the expected result for Filmic. Setting it to Raw won't give you your expected result either, however. Simply setting it to Default should do the trick.
But then of course you'd be giving up all the benefits of Filmic, which is probably not what you want. Basically this is normal and you shouldn't worry about it, as long as you are going for a realistic render, stick to Filmic and just have faith. If you're not going for a realistic render, then it might be worth considering switching back to Default color management.
