The main “purpose” of the raised degrees in ascending melodic and harmonic minor is to create a strong leading note:
X:1
L:1/4
M:none
K:Am
V:1 clef=treble
e ^f "V₇ ↗"^g "i"a
%
Clearly, this leading tone only makes sense if you actually do resolve it upwards. If you go down instead, this can rather leave a feeling of unresolved tension.
X:1
L:1/4
M:none
K:Am
V:1 clef=treble
a "↗"^g "?"^f "??"e
%
In harmonic minor, this unresolvedness is not as apparent because the attention will be more drawn to the exotic (if not somewhat jarring) 1½ tone step:
X:1
L:1/4
M:none
K:Am
V:1 clef=treble
a (^g "!↘"f) e
%
Melodic minor avoids these 1½ tone steps to create smoother melody lines. When going up, you still want the leading tone, hence you raise the ⅶ and also the ⅵ. But when going down, it's more sensible to just leave both of them natural.
Of course that doesn't mean you can't use raised ⅵ and ⅶ degrees when going downwards. In particular if one voice already has one of these raised tones, it would be problematic to un-raise them in another voice. For example, the fugue that RRR brought up has this passage:
X:1
L:1/16
M:C
K:Am
%%score (T1 T2) (B1)
V:T1 clef=treble
V:T2 clef=treble
V:B1 clef=bass
% 1
[V:T1] (d8 d2 )
[V:T2] A,2dc BA^G^F E2
[V:B1] G,2^F,E,F,2^G,2 A,2
Here, the bass is already going up in melodic minor to the A root, and especially if the bass does this you really want the leading note effect, so it is F♯-G♯-A. At the same time, the alto needs to cross the ⅵ / ⅶ territory to get down to the Ⅴ (e). Using a g-natural there would cause a pretty bad clash between the voices:
X:1
L:1/16
M:C
K:Am
%%score (T1 T2) (B1)
V:T1 clef=treble
V:T2 clef=treble
V:B1 clef=bass
% 1
[V:T1] (d8 d2 )
[V:T2] A,2dc BA"⚡"GF E2
[V:B1] G,2^F,E,F,2^G,2 A,2
On alternative would be to use harmonic-descending there
X:1
L:1/16
M:C
K:Am
%%score (T1 T2) (B1)
V:T1 clef=treble
V:T2 clef=treble
V:B1 clef=bass
% 1
[V:T1] (d8 d2 )
[V:T2] A,2dc BA^G"¿¡"F E2
[V:B1] G,2^F,E,F,2^G,2 A,2
but again, that sounds a bit Spanish. Especially in a middle voice it's more innocuous to just adapt to the context of melodic-minor from the bass voice there, even if it means traversing the scale in the “wrong” direction.