Certain Eldar craftworlds DO have standing armies. The guardians are the citizen militia - their unit leaders are often those who were once warriors, but chose a different path afterwards.
Biel Tan comes to mind. They are also more "aggressive" in the "defence" of their lands than the others (showing no mercy to interlopers in their territory).
The harlequins fight because they know the threat chaos holds for all. They fight against chaos. They also act as their race's memory, keeping its tales alive with theatre and interpretive dance.
As for the aspect warriors, they each fulfil a role as well as representing an aspect of the Eldar psyche (as well as an aspect of their god of war - but the one and the other are intertwined).