I'll be a little diplomat here, both points of view add value to the thread as well as address the OP's concerns.
The point that using good quality original spec wiring would be more than sufficient to last the remaining life of the car is correct and well taken. Though, suggesting the use of materials that exceed spec supplemented with techniques and protection that address conditions that had some affect on the failure are also quite valid, not necessarily incorrect and are certainly worthwhile to point out.
While I would probably opt for the factory spec system (in this case) I'm glad to have learned about the protective quality of fiberglas tape and the explanation of wire gauges will be useful to many readers.

I'm curious though, as I'm not so electrically knowledgeable. Can't over-gauging wire pose a potential threat to some more delicate instruments and sensors? That is, some wire gauges are actually chosen to cap or restrict the flow of juice (provide resistance) and using a larger gauge wire might allow too much amperage to flow though components (particularly computers and control units) that aren't rated for such flow. Maybe I'm wrong about this or maybe it doesn't really apply here, just curious.