The main reason I do a double flip almost always (sometimes I don't...if the UIC says one flip, it's one flip) is a throwback to the honor of the old original Knickerbocker Rules. rule 3 says, among other things (and this is a paraphrase) that the two teams will toss to determine who calls it, and then there is a second toss.
Not trying to be an elitist...just my little quirkish deference to the roots of the game.
Of course if I wanted to get to the REAL roots of softball, I could use the rule from the 1890s that allowed the leadoff batter to run the bases either clockwise or counter-clockwise.