Wind speed is a significant factor in landing distance because the effect of wind may not be a 1:1 relationship with distance (GS) as you imply
Stretching the memory way back to simple mechanics in secondary physics courses, most of us can recall something along the lines of
s = (v^2 - u^2)/2a
which, for a first approximation consideration of a landing (and quite reasonable for the ground roll bit) simplifies to
s = v^2/2a
where
s = distance gone
v = initial speed
a = constant acceleration (deceleration)
ie to a reasonable approximation, distance varies with (ground) speed squared. Hence the very real concern with getting everything right for tailwind landings ....
When you see simplified approximations for distance variations along the lines of so many feet/knot, such figures are based on straight line approximations of the realworld relationships and should only be applied for small speed variations.