If you try a triangle test with sugar and syrup Daiquiris (i.e., two of one and one of the other) you should be able to pick the odd cocktail out with regularity. They are different, albeit not dramatically so. If you give the sugar a quick stir first you shouldn’t get sugar at the bottom of the cocktail glass; I never do, anyway, not with plain granulated white sugar. Other kinds can be much more difficult to dissolve.
There are a number of classic cocktails that, in their original form, call for what are now aberrant or at least non-standard techniques. The Julep, as I mention, and the Sazerac, as you do, but also the Old-Fashioned, which people are always trying to police these days, whether it’s just by using syrup or by making the whole thing in the mixing glass. There are others.
When I first started writing about drinks, I used to spend a fair amount of time trying to rationalize such drinks but now I tend to regard any such artifacts of technique as a gift; as the dead hand of some past bartender reaching forward and handing me a drink. There are many paths through the woods, as the saying goes, and these days I appreciate knowing another one more than I do some incrementally increased efficiency in navigating one I already know.