My electrician put the metal plates pictured below wherever he drilled through a stud. My guess is that this strengthens the stud, because it was weakened by the holes he drilled.
Studs with metal plates added:
This is excellent practice. These plates help guard against someone accidentally drilling into the wire when mounting things on the wall.
Nothing to do with strength of the stud. Everything to do with protecting the wire.
A necessary safeguard in this case because the wires come too close to the edge of the stud - vulnerable to drills, screws, and nails.
Not normally required if the wire is in the center of a regular 2x4 (should never need to drive a nail or screw that deep).
