Des, I didn't look away once .... I found your explanation perfectly 'expert' enough, and you raise the interesting point about how flash power is actually controlled, which can be tricky to grasp. The natural way we might think is by actual power supply control, sort of like a light dimmer dial. But that's for a continuous light source. With flash it's the amount of time it is on for that determines how much brightness is recorded, so as you say, the very shortest (low 'power') settings help to freeze action ..... The problem with it is that it's a small amount of light, so as you say also, works best when mixed and just filling in with the main ambient exposure.
This is the explanation for why HSS does not freeze action well, despite many people new to flash thinking that it might .... The light source for HSS is effectively a continuous burst, in rapid pulses, and so its duration is fairly long compared to normal flash bursts. Even at exposure times of say, 1/4000 - 1/8000 secs it's effect is diminished by the high power loss during HSS at such speeds.
I use the Gary Fong Powesnoot to bring back lost output during these more extreme HSS ' moments', but its perhaps more suited to closer subjects than wildlife.