The frayed tips give a white cast to the lawn. And the white frayed tips never go away unless you mow with a sharp mower blade and remove the frayed tips.

And those same rigid tough cells not only make cutting tough, they make mower blades dull! It is a double whammy you need a sharp mower blade to cut the grass and the grass is dulling the blade. But many homeowners never sharpen mower blades (who would think that in the fight "Steel Mower Blade vs. Grass" the steel mower blade would lose).

With St. Augustine being a wide bladed stiff southern type grass, I don't think that you'd have any trouble cutting it good and clean in one pass with just about any ztr brand as long as you keep fairly sharp blades.
It has been my experience in my lovely state of Arkansas that 80% of the properties I manage the mower that cuts easily and discharges well. I use a Kubota ZD331 on most of my properties when cutting St. Augustine. But my Scag or Exmark Ztr's will do a good job as well. Pretty much any mower will do as long as the blades are sharp.

Good luck with your choice of mower.