A common goal in rescue work is the KISS principle. Simpler techniques are often faster to set-up and have less points of failure. A great example is mechanical advantage systems. The Armstrong method (simple pulling) is very easy to control and has very little set-up time. Compare this with Z-Drags and Pig Rigs which have a number of knots, require extra equipment, have weaknesses at bends, and require multiple safety countermeasures. Once the boat is freed, the Armstrong method is quite adaptable and easy to clean-up as well.
The rescuers safety is also paramount. Before jumping into a fast moving rapid, take a few seconds to consider some alternatives. Can you reach effectively with a stick or paddle? Is it easier to traverse in the slack water above or below? Many of us carry two rescue ropes, a wearable and a larger one in our boats. Often, we can stabilize a situation (buy time) with the smaller and available rope and do so safely from shore.
Time is often a critical factor in rescues. The boater that is currently pinned heads up may soon tire and flip. Foot entrapments almost always require quick rescues. In advanced whitewater, we strive to get swimmers to safety ASAP to avoid fatigue, injuries, and flush drowning.
When you think of speed versus safety, we sometimes need to make an educated trade-off. If a person is pinned heads down, you need to get someone to the victim ASAP and that probably means paddling and sometimes ditching your boat if necessary. Others in your group can work in parallel heading downstream, upstream, and getting safety gear. On the other hand, there is no reason to hurry when unpinning a boat. Take your time and take as few risks as possible - boats can be replaced.