I ferment my beer and usually let it sit on the primary cake for quite some time. Mainly because I am busy with other things. When my beer comes out of the fermenter I have learned to recognize it as being good or great but without carbonation.
I think that what happens in the bottle is that you get a slight amount of oxidation that you can't control/prevent. Not all oxidation is bad, and this might help with that maturation flavor you are thinking of.
Secondly, I think the addition of CO2 starts to bright the beer up a bit too as a the beer's acidity increases a bit too. I think the lack of CO2 and what it does to the beer is the real contributor to the green character.
Albeit these are small changes but they help to round out the flavors and start to create a harmonious experience in the beer from all of its parts. (Sort of like soup the day after you make it)
That said I don't think there is one true answer for this. These are just my thoughts, which is why I chose to also make this answer a wiki.