Correct me if I’m wrong:
monitors can’t show linear space with full midtones. If no gamma-correction is applied to an image, it will look too saturated and dark.This may be the reason why so many renders look too saturated and contrasty, because people are unaware of gamma-correction and how to use it.
But why we don’t see pictures in photoshop etc with wrong output then? Because software like photoshop uses color profiles and applies gamma-correction (?). Or do the digital cameras apply gamma-correction when creating the images? 
Your monitor, when you are rendering something, shows you by default wrong output, because it cannot for some reason (maybe we just have bad monitors)
show linear space with full midtones. So this is not “I use it because I like it”, or “I don’t like it, so I’m not gonna use it”. You should use it (be aware of it) always. Amazing that this very important subject is not explained in many beginner’s books.
What you are doing by applying gamma correction is you force your monitor to show you correct linear result, and that’s it. No magic here.
When you save your renders as 32-bit floating-point image, you save it without gamma correction, because you will apply it in post-processing that algorithms would work with linear space (I may be wrong about whether it works better with linear space).
Why this it not by default in rendering software? Maybe because it’s more clever to save renders are 32-bit floating images, so this is not needed in this case. But we still need to view while rendering the gamma-corrected result to view it correctly. It could be a switch button there damnit.
So one good way to see if your gamma is wrong, just save your rendered image as HDRI and open it in photoshop, and you will see whether it differs from what you see in your rendering viewer.
So what you should do:
save your rendered image as hdri and open in photoshop and see if it differs from what you see in your rendering viewer. If the HDRI looks washed-out in photoshop, then your gamma is wrong
find out where in your software gamma-correction is
use 2.2 gamma when you are rendering in 8-bit per channel image, it should look just as your HDRI verion in photoshop
use no gamma-correction (1.0) when you are rendering in 32-bit floating image, hdri or exr etc
there also an issue with bitmaps, maybe someone could explain it: what adjustments must be done to bitmap files? As fas as I know, some renderers do it automatically. I just use 2.2 for input and output for bitmaps, and it shows me what I see in photoshop. Would like to hear a better explanation.
