It’s more related with ‘apply minimal force needed’ than with ‘make small movements’ per se. Small movements is just a consequence.
First of all everybody who plays fast use small movements at some speed. Look at Troys slow motion videos. The faster he plays - the less his movements. Why? Simple physics.
When something massive oscillating, force needed is roughly proportional to an amplitude and square of frequency. Since we can’t change frequency (t depends on tempo) all we can do is to decrease the amplitude.
Why keeping minimal force is matter? First, stamina - I’ve seen some guys here complaining about not being able to play fast for a long time, even when doing simple tremolo. For me it’s not a problem at least up to 250bpm. Second - avoiding injuries - and this is much more important. Using excessive force is no good. Like really. Third - at some speed you just can’t apply enough force to move your hand far enough.
Basically, up to some speed we can dose applied force quite precisely thus controlling a song’s dynamics. But beyond some tempo we can’t do it. All we can do is to keep this force more or less constant, or at least not very large - and that’s why everybody instinctively decrease their movements amplitude on faster tempos.
So, ‘small movements are fast’ is actually true. Well… at least if you are not an adept of some kind of alternative physics. But keeping small movements all the time is kinda strange. It’s like driving your car using 5th gear only. And vice versa - avoiding small movements is like avoiding 5th gear. Well, you could do this but don’t ask then why your car is not fast enough.