Is this the only DT album without a "ballad"?
I guess it depends on how you define "ballad." I would say TOT doesn't have one.
Mellow song ... "Vacant"?
Well...that's why the definition is important, and I understand that a lot (and maybe even most) would regard Vacant as a ballad.
I don't think Vacant is a ballad.
I don't think there's any ballads on Awake, SDoIT, and Systematic Chaos either. I don't consider Space Dye Vest or Disappear (or Goodnight Kiss section of SDoIT) to be ballads.
Ballads for me are: Another Day, Anna Lee, Through Her Eyes, The Answer Lies Within, Wither, Beneath The Surface, Along For The Ride, etc...