I do not see how protection is optional when wiring is so close and does not meet the distance.
Because the requirements within 300.4 depend on both location and direction of travel of the cable.
Now 300.4 could just say "any portion of any cable within 1-1/4" of the edge of a framing member shall be protected." That would be a requirement that is based only on location, and that seems to be how you are reading 300.4. But that's not what 300.4 says.
Instead we have requirements based on both location and direction of travel. For holes in a framing member closer than 1-1/4" from the attachment face of the framing member, we are required to protect the portion of the cable within the framing member; there's no language about extending that protection to 1-1/4" past each edge of the framing member.
Likewise, for conductors installed parallel to a framing member, we are required to protect the cable if it is within 1-1/4" of an edge of the framing member. But that doesn't apply to cables traveling diagonally, they can be closer than 1-1/4" from the edge of a framing member without requiring additional protection.
So say you have a 2x4 wall and you have a box that extends 2-3/4" into the wall framing, with a back corner box entry that is say 1/2" from the wide face of the stud (and 3/4" from the wallboard behind the box). So you route your cable down the middle of the wide face of the stud, that complies with the 1-1/4" requirement, until the cable is within say 3" vertically of the box. Now your cable bends to a diagonal route to the box entry, it travels diagonally 3" vertically, plus 1/2" away from the stud, plus about 1" towards the backside of the wallboard. That diagonal section is not subject to the 1-1/4" distance requirement.
Now you could route your cable less carefully and thereby trigger 300.4(D) protection. For example, if the diagonal jog described above doesn't occur in the vertical region 0" to 3" away from the box, but instead occurs between 6" and 9" away from the box, then the first 6" out of the box would be installed parallel to the framing member and would require additional protection. But the simple solution is don't do that.
Cheers, Wayne