Every boat has a moment when the engine is more nuisance than help. Maybe it won’t start, maybe it shouldn’t, or maybe you just don’t want a spinning prop anywhere near a tired swimmer. Either way, the sea doesn’t pause while you sort it out.
Under sail, a person overboard is a helmsman’s problem first: keep them in sight, keep the boat under control, and keep the crew doing one thing at a time. The trick isn’t the big turn; it’s arriving the last few boatlengths with just enough way on to steer, and not one knot more.
If you can do that calmly, the rest becomes seamanship instead of luck.