Except that the “Novus Ordo” implicitly prohibits them. Maybe the problem isn’t the Novus Ordo, but the poorly catechized people in the pews (and, often enough, the poorly trained man at the altar).
Without hopefully being accused of bashing, I would like to point out that the new rite was supposedly designed for (and to produce) mature Catholics who knew their faith. We all know the statistics of pre-VatII Catholicism, we are supposed to be in the "new springtime".
The new rituals were designed to produce more priests and religious along with a better educated laity, that has not proved to be the case. Yet we're still merely tweaking things as if that's all that's needed to end the frost of winter. A winter that for some reason or another coincided with the introduction of the reformed liturgy. I know correlation is not causation but the circumstantial evidence is pretty dire.