There are complex trade offs when thinking about stopping HIV treatment. This is one issue that crystallizes what makes this complicated. Hopefully I can make it more clear.
As you note - when HIV grows it preferentially attacks the cells in our system designed to combat it. Which is why the research on boosting the immune response for those treated very soon (a few months) after infection uses an approach of only briefly stopping meds. In that approach, the battle between our immune system and HIV is used to stimulate those cells to grow, and then stopped when we fear we're losing - when the desired expansion of our cells in response to battle is leading instead to exhaustion/depletion of the very cells we are trying to create. When this transition happens is sadly not clear and there is no precise way yet to know which way the battle is going - except with fancy lab tests not widely available, or perhaps by measuring the viral load. If the viral load is stable then we're likely OK, but when the viral load is steadily rising, we're likely losing...
So - when we stop meds - these HIV specific cells are called into battle. The problem is that these cells are often severely damaged, even eliminated, some months after seroconversion in most people. So for the many people who didn't start treatment until years after HIV infection occurred - there may not be too many of these cells left. So, if that is the case, this concern of "preserving" HIV specific cells may actually be far less relevant - at that point, stopping meds to avoid toxicity may be far more important in determining what to do, rather than worries about preserving cells that may just not be there anymore...
Now, there is research to see what we might do to recreate these cells. Since, when present in "ample" quantity, they may be able to restore some degree of control and suppression perhaps even in the absence of treatment. And research is using not only med interruptions, but also various therapeutic vaccines to try and recreate these cells. But for now this is proving to be an elusive goal...
So - in sum, I'd think this article simple summarizes one side of the coin, relevant primarily to research done for those who are likely to have these HIV specific cells intact - those treated after acute HIV infection was diagnosed, and perhaps those whose cells were intact after that initial battle - likely to be those with a low set point after infection. For others, it is probably just one less problem to put in this complex equation of what to do...