Why don't we consider the reduce cross-sectional area while calculating stress in a metallic wire?

The change in cross sectional area can be considered by differentiating between Engineering Stress/Strain and True Stress/Strain.

Engineering stress is the load divided by the original cross sectional area. Engineering strain is the change in length divided by the original length. These are convenient and useful approximations when dealing with small deformations and linear elastic behavior following Hooke’s Law.

True stress is the load divided by the instantaneous cross sectional area and true strain is the incremental change in length divided by the instantaneous length, I.e. the length at the start of each incremental change, not the original length. These may be used for accurate description of plastic behavior.

The two types of stress/strain are generally the same in the region of linear elastic behavior.

Hope this helps.