Making the bullets shorter and lighter worsens the BC but actually makes them more, not less stable.
Maybe with subsonic ammo like air rifles and possibly shotgun slugs, but not with most centerfire ammo. Bullets lose their stability when their speed slows to a certain point, usually about 1,000 fps. Bullets with better BC maintain that speed much farther downrange, and are stable longer.
Short lightweight bullets start faster, but a heavier bullet with a better BC will reach a point downrange where it is moving faster even though it may have started 200 fps or more slower at the muzzle.