All perfectly valid points. However, those odds do go up dramatically in the conditions faced when going offshore (at least, more than "nearshore"). And to make matters worse, what those concerned with safety, search and recovery try to emphasize, the farther offshore you get, the fewer search and rescue resources are available that can get to you, and the longer it takes to get to you, not to mention being able to find you at all.
We don't even put all our trust in the jacklines alone. If we have to go forward in challenging conditions, we do it on hands and knees, and still hold on to some part of the boat.
a. I have had tethers catch me numerous times. That is because I use them as a third hand to lean against in many circumstances, where they reduce the chance of a stumble , slip, or slide. In fact, by keeping the slack out of the line, I make it safer. This is mathematically provable and obvious.
b. If you cannot trust the tether and jackline implicitly with your life in all circumstances, then there is something wrong either with the engineering or you understanding of it. Climbers and rope access workers do this every day. Check that the rigging must be
right, then relax. But there should be no risk of failure or thought of the same in your mind. None.
Yes, for many sailors the need is rare. I've never needed a PFD either, but I won't argue the need to have them on board and that they work properly in all conditions. In fact, I've never needed a PFD, but I have needed tethers. To my mind, if the maker is going to advertise a boat as storm worthy and not include jacklines and anchor points, they are lying. It isn't storm ready by any working definition.