Smell is enhanced when the scent can linger or held for extended periods of time (additional seconds improve the ability). Birds do not have that luxury.
Since the airsack-system is far more efficient than our lungs when it comes to extracting oxigene from the air - why not the same with smell?
(air passes through the lungs to the hind airsacs first -then back again to the front airsacs and then out into the open.
2 breaths for one

(scientists have been wrong about the 'birdbrain' a lot already, so maybe the olfactorypart is also more dense and intense than we know ...)
my thoughts: if prey animals have a strong smell about them -> they get caught easier.
(it is easy -for a human- to smell a fox hiding in the bushes near you but sniffing out a bunny is nearly impossible)
but... most parrots have a rather distinctive odeur about them, some are quite strong.
That you see with animal that communicates (partly) by smell.
My macaw is weird (
in my experience! It might be normal macawbehaviour- I do not know. She is my first close-up&personal bird of that sort.) that she wil release that certain oversweet aged flowery smell on certain occasions...
just before a bath, when she is busy impressing a friend of mine etc.etc..
(Since she loooves the bathing it is not a fear response

but it happens when she gets excited.)
Evolutionary speaking that would be unwise (releasing strong smells alerts anything around you, friends and foe) but as a form of communication - spot on!
I have not been lucky enough to be able to smell amazons longterm, but if they also "whiff on occasion" I think they may be communicating that way too.
(that implies their sense of smell is pretty good and probably is also used in the other areas as foodgathering and gnawing out nests)