I know that studs need metal plates over studs where there is plumbing
too close to the wall. This is to protect a nail going into the
plumbing.

Those little goodies are about as cheap as they come, and spending a
buck and saving a whole sheet rock replacement job (including
retexturing and painting later) is a REAL no brainer to me.

When we built our house a few years ago, I installed metal protection
plates everywhere code required for pipes, wiring, etc.

The one area I was surprised a plate was "not" required was on the back
side of an electrical box. In a 2x4 wall, with a deep box, the cables come
out of the back of the box within an inch or less of the stud face. It
seemed all too easy to me for a drywall screw or other fastener to miss the
stud and pierce a cable where it exits the box. Or for that matter, to
drive a screw right through the backside of the plastic boxes. There were
no ready-made protector plates for this situation, so I bought a bunch of
blank cover plates that are made for 4" electrical boxes, and screwed those
to the backside of the wall studs. It usually took 2-4 of the 4" plates to
protect each box.

The electrical inspector said they weren't needed, but for less than $20
for the whole house, it seemed like cheap insurance. It did no harm to add
the extra plates, but could prevent a major problem later.

Anthony