I don't think that's what he means by consistency...
There is a fair amount of agreement among strength coaches and powerlifting coaches that fatigue seeking routines are deleterious to gains. You will get stronger that way... for a while. But at the very minimum, we do better by training reasonably heavy and avoiding neural fatigue. Going balls to the wall in the gym at every session is not a good way of avoiding neural fatigue or producing long-term strength and longevity, generally (there are always exceptions).
I agree with you 100% that progressive overload is important (as in progressing in weight/reps). However, consistency is key in terms of establishing intelligent work sets that aren't maximum capacity. Power to the people and Periodization are good reads for understanding strength. Just because something yields results (for a time) doesn't mean its the best route. What TS expressed of seeking soreness is generally accepted as broscience, as is consistently going to failure.