The Church seems to be relatively silent on this matter. However, just because the Church is silent does not mean something is permitted. After all, no document states the laity cannot stand on their heads for the Our Father during Mass, yet we’d universally consider it inappropriate to do so.
The general rule of thumb to remember is: “no other person, even if he be a priest, may add, remove, or change anything in the liturgy on his own authority” (Sacrosanctum Concilium, 22.3).
So the question for us becomes: is the orans posture an addition to the liturgy?
In my opinion, yes. My reasoning is that the General Instruction of the Roman Missal references the orans posture with the phrase “with hands extended.” It is instructed to be done twenty-eight times and is used as a direction only for the priest(s)—the laity are never directed to pray “with hands extended.” Given that it is clearly a directive in the GIRM, to add it to any other part of the liturgy would be a violation of the above stated liturgical rule.
As to the reason why this matter is rarely addressed, that most likely has to do with pastoral sensitivity. If a handful of people are innocently praying in that position, the priest is not going to go out of his way to embarrass them or cause them to feel uncomfortable. Their action, while not liturgically correct, is probably not a distraction to anyone around them.
The only time I could see a priest feeling pastorally required to address such a situation would be if people were being instructed by others to use the orans posture, or if it was so widespread that those who chose not to do so were made to feel uncomfortable.
For more information, see this article.