I'll throw in another variable to the throw rope fire. Wigston was the first to introduce me to the idea of setting up safety downstream at a point on shore where you want to pull the swimmer into, rather than planning on the traditional pendulum. I rarely see people do this, much less discuss it.
I've given this a fair bit of thought and think in many, if not most situations, this is a much better strategy that avoids a lot of the above mentioned problems with deploying a throw rope to begin with.
I can think of a one situation in particular that was just a classic rescue scenario where a swimmer was hanging onto a cliff wall on river left and needed to get brought back to river right. It was a small creek and the river right bank had tons of good access points. I suggested to the person upstream that we should pull him into an eddy downstream of the victim. I was overruled in favor of the traditional pendulum. What happened was when we victim jumped back into the water holding the rope he became stuck in current shy of an eddy on shore, holding on and planing out. I forgot how, think maybe I vector pulled on the rope or something, but got him in, but not quickly or easily. Compounding the situation was that he had wrapped the rope around his hand just before he jumped in. I saw him do it, but it was too late for me to yell at him to stop. Fortunately a fairly bad laceration from the rope was all that happened to him.
I heard a podcast recently talking about how it takes a certain amount of momentum to override a lot of things that are conventional wisdom, even when evidence points to a different course of action. It used the example of shooting free throws. Apparently the best free throw shooters in the world have always been underhand shooters, and there's a lot of evidence indicating this is the best technique. But people still insist on shooting overhand because that's how it always been done and it's not a 'granny shot'. I think the pendulum strategy fits this same tendency.