Why is a Sazerac rinsed with absinthe, not mixed with it? The spec and a rinse builder

Ingredient	Measure
Straight rye whiskey	50 ml (1.7 oz)
Sugar cube, or rich syrup	1 cube (about 4 g), or about 7 ml syrup
Peychaud's bitters	3 dashes (2 to 4 is normal)
Absinthe, or an anise liqueur	a rinse: swirl and tip out
Lemon peel	1 strip, oils expressed over the top

Specs vary. The IBA version uses 50 ml cognac, one sugar cube, two dashes of bitters and 1 cl of absinthe for the rinse; many New Orleans bars use rye and an anise liqueur called Herbsaint.