Why in semiconductor studies, we are only concerned with reduced zone representation of e-k diagram?
Electron transistion can happen anywhere in the semiconductor structure.

The first Brillouin zone is defined in the reciprocal space. Theoretically, all atoms in the original crystal contribute to the "image" in this reciprocal space. So I believe you may have misunderstood what the Brillouin zone represents.

So everything happening in any Brillouin zone theoretically represents the whole crystal.

So it does not really make sense to say "transition outside the Brillouin zone". The whole crystal is mapped to a cell in the reciprocal space, and a single cell has an effect on all cells in the reciprocal space. So if you look at a single electron in the reciprocal space, then the image of that electron is also there in all Brillouin zones.