That works for a second, but does not get fish to come to you.
Agreed.
The best teachers on how to approach fish are the predators. Look at how groupers blend in and seam to float effortlessly toward their targets. Small and slow movements, using body orientation, currents and surge rather than fins to move.
Move slowly using the tip of your fins, glide a lot, do not use your hands, and do all big camera/strobe/buoyancy adjustments before you even start approaching your subject.
(Now if I could just manage to not suck at composition...)