Having just re read your post.. are you talking about Amer. style F/T ?..

There is a distinct difference to the approach of " sway " in that context .

Whe I first worked for F/A, there were some very strange ideas on how to employ sway on certain types of movements ( it started to look like a rocking chair ! ).

As to balance being important in sway.. its important in everything we dance .

As Scriv. said ( again ) sway is a " natural " element that appears on most fwd movements combined with " swing " and of course, in various other advanced figures .