Well, just to present the contrary view, I've always kept the original harness, even after a meltdown and/or ill-advised modifications by the previous owner. My previous 59 TR3A suffered a meltdown around 1985, so I ran new wires (all red since that's what I had on hand and I wanted to drive the car to work the next day) to the headlights and went on. The rest of the harness was still working fine when it got wrecked in 2005 (and I still rob wires from it on occasion).
The original wires on my current 56 are faded until the original colors cannot be seen; even the places where the original woven outer jacket hasn't fallen off, it's just a uniform brown. Can't even tell if it originally had a tracer or not. The previous owner removed the control head, and lopped off the harness wires to it; so one of my first tasks was to patch in new wires (robbed from the 59 harness) for that.
Unless you modify it heavily, there is nothing "safe" about the original wiring harness or a new reproduction. There are a lot of unfused wires running around, any one of which can cause a fire if it rubs on a sharp edge or whatnot. So new or old, you have to make sure that doesn't happen.
It's also easy (I find) to add wires for whatever modifications you want to make. I've done a lot of that; at the moment I think I'm up to about 9 relays, 6 additional fuses and a couple of circuit breakers (for the headlights, arranged so one breaker can only kill one light). (Yeah, I probably went overboard on the relays, but they are cheap and easy. 3 of them let the rear corner lamps do triple-duty as tail/turn/stop lamps; while I used 4 relays to feed the headlights. None are visible to the casual observer, except the OD relay mounted in the stock location.)