Progressive overload is a fundamental principal of weight training. The problem is how strong can you get? I trained with versions of HIT for many decades. It sure worked. I would cycle my training and each cycle try to get stronger. Of course there is finite limit to what anyone can do. If I got near my best weight I knew I was doing good.
What you can progress in for a long time is in muscular endurance through volume. If you are doing 5 sets of say 12 reps. Maybe for weeks you cannot get all 12 reps for the five sets. You can work on your progression to complete the goal of 5 of 12 then you can increase the weight.
I also believe a big mistake is to start a training cycle using maximum weights. It leads to burn out.
Great post.
I actually use the volume method you described for the majority of my training. I use 4 sets of 6-8 reps with the same weight or 3 sets of 9-12 with the same weight depending on the exercise. And 3x8 or 2x12 for isolation work.
On the first exercise of every workout I pyramid up to a top set, either 3x8-12, 4x6-9, 6x4-6
For example last night's workout:
Front squats: 155x12, 210X11, 260x8 one to five minute rest between sets
Close grip incline press: 155x6, 185x8,8,8,8 two minute rest between sets (will move up to 195 for next workout)
One arm rows: two minute rest between sets 80x8, 100x10,10,10
Hanging leg raises: one minute rest between sets 8,8,8
Rear delt raises: one minute rest between sets 25's x 12,12