This is wrong about the Doppler effect and perception of distance.
It would be correct if the object moving and emitting sound
as it moved were coming straight towards you and going through
you and then moving away. But a police car with a siren say
is not aiming straight at you(or at least you better hope not!)
It is going by on a straight line that has a closest point to you
but that closest point is not you! So the amount of pitch shift
in fact changes continuously, being a max shift up when the
car is far away, diminishing gradually until the car is as close
to you as it will get(at which point the car is not changing distance
from you at all  in the instantaneous sense) and then gradually
as the object moves away with increasing speed relative to you!
the pitch falls to a minimum.
This is not dependent on mel shifting with level--it is
literally the case on the frequency level. (The mel shift
would be the same whether the car were approaching or departing--
just reversed in time. This as I recall is not what is observed--
the situation does not have time reversal symmetry)
Robert

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