I bet that the tether is rarely the weak link in the system. I think the weak link will be the crummy chest harnesses that seem to be everywhere. They look easy to slip out of. I also think that the jacklines deteriorate much faster than the tethers because of UV exposure. Finally, I think most jackline securing points are not really bombproof. Using a piece of rope for the tether is fine in my opinion. They key thing is to be able to undo it, under load, at the person end in case you get trapped somewhere where you don't want to be.
There is a tide in the affairs of men,
Which, taken at the flood, leads on to fortune;
Omitted, all the voyage of their life
Is bound in shallows and in miseries.
Shakespeare, Julius Caesar IV, iii, 217