Stoney W/S is important in all manuever performance equations, specifically in turn rates and radius and climb performance. All other factors equal it is the deciding factor.
Rmin is direcly proportional to W/S, OMEGAmin (turn radius) is inversely proportional to W/S, Corner Speed is proportional to SQRT(W/S), Max N is inversely proportional to W/S (independent of actual structural integrity as an a/c could have a CLmax which would combine to push it over the edge - stress wise)
I'm not discounting the effects of low wing loading on those performance examples you mention. I'm merely saying that wing-loading, by itself, is not the best way to compare two aircraft and their relative performance, without taking into account all the other variables. On this board, a lot of folks that are not as well-read as others, quickly jump on wing-loading as the number one performance metric, and then have a hard time understanding why a 109 could theoretically have a larger sustained turning radius at 30,000 feet than a Jug, for example.
[EDIT] At sea level, standard conditions, the Power Available/Power Required math is more simple, and ultimately, this is what controls performance, not merely the aircraft's wing loading.
[EDIT2] Also, climb performance is maximized with excess power. The aircraft with the most excess power will climb faster. Now, low wing-load helps because it reduces the amount of power required, but if a heavily wing-loaded aircraft has more excess power than a low wing-loaded aircraft, the aircraft with the higher excess power climbs faster. Just another example of why wing-loading by itself is a poor performance characteristic to compare aircraft with. Again, this is illustrated by the heavier, more highly wing-loaded Jug having better climb than say the lighter wing-loaded 109G at high altitudes, for example.
