The proposed use is MDMA-assisted therapy. Take a dose, talk to a therapist. Wait a month, repeat. You seem to be imagining people popping the stuff like SSRIs.
Intuitively, this makes a lot of sense. MDMA is a fun drug because of the fact that it makes it basically impossible to feel negative emotion under its effect. PTSD is characterized by extreme negative emotion around a particular trauma, to such an extent that it becomes disruptive to living a normal life. Just talking about the traumatic inducing experience can lead to uncontrolled emotional responses, making it difficult to approach therapeutically. The MDMA acts as a shortcut around that last bit: by blocking the patient from feeling negative emotion while they talk about their trauma, they can re-evaluate it in a more removed way.
Combine that with theories about how we edit memories when we recall them, and you've got a pretty obvious method of action.
It's not intended to be a chronically taken treatment. But the results were pretty massive. That CAPS-5 score they talk about the reduction by 24 points versus therapy alone's 15 is on an 80 point scale, with the bare minimum for PTSD diagnosis at a 12, and "moderate" PTSD being in the 23-35 range.
Compared to most results coming out of the mental illness treatment field, MDMA's looking like a silver bullet.