replacing the entire piece of wire may be 'better' but repairing with tubing can be 'acceptable or safe practice'. repairs with shrink tubing are made all the time in the industrial world for these types of incidents. if doing a shrink repair, it is important to use an appropriate tubing, one with a ul listing that has a voltage rating. also need to prepare the conductor and apply the tubing in accordance with the manufacturer's instructions. installed in such a manner, the tubing repair is totally fine. the problem comes in when joe homeowner is using some cheap tubing off of ebay or not installing it in the correct manner.
i'm with you though, i would replace the entire conductor for such a short length and small gauge.