Well, none of us is "sure" of anything, but my reasoning comes mostly from the fact that miniaturization seems to be caused by a chronic exposure to androgens(or maybe some other unknown factor, like the buildup of fibrosis). It is not something that is "programmed" in that tissue by default, the opposite is true, that's why you used to have hair there. And since we're damaging it and (theoretically) allowing it to regenerate fully without scar tissue, it should be regenerated according to the original "blueprint", not exactly how it was before.
For example, let's say you acquired a Gecko super power that allowed you to regrow limbs upon activation, and that you have a scar in your hand, some acquired moles from sun exposure, or even a tattoo. If you ever lost that arm and grew it back, do you think it would have any of those traits? If this power is following a "Biological logic", it shouldn't. In the same way that dyed hair grows with it's original color, rather than with the new color you dyed it with and the reason why people "damage" their facial skin with lasers and acids to make it look younger, by regenerating it with finer wrinkles. You said it yourself: "facilitate the STEM cell".
Of course, this would mean that those hairs are still vulnerable to DHT, but given that many are willing to use Anti Androgens or that some miniaturize quite slowly it might be worth it. Also, depending on how many treatments are necessary or if infrequent maintenance sessions are safe and effective, it might be preferable to and cheaper than having multiple hair transplants. Healing works much faster than miniaturization.
This is why i don't think very androgenic hair(like beard/body hair) is the best test candidate for this effect. Or even if it is a decent one, it might not be immediately noticeable.