Giving a third dose of the vaccine would probably also give people in the two-dose group additional protection against the Delta variant. The question is whether that additional protection is actually worth the additional doses of vaccine required and the side effects. There are arguments in the mainstream media that giving those extra booster doses would be outright immoral because they could be used on people in the developing world who haven't been vaccinated yet; those arguments never get applied to requiring the previous-infected to get vaccinated, presumably because vaccination is a partisan political topic.