Q: Are the inserts for the Eucharistic Prayer used ONLY when the Ritual Mass is celebrated… or whenever the sacrament is celebrated, no matter the Mass used (for example, if the Mass of the Day is used)?
A: The rubrics aren’t clear on this point, but I see no problem using those inserts on days when the Ritual Mass cannot be used.
There’s a bigger issue with the three main presidential prayers and the preface. If your bishop celebrates confirmation in a parish on Wednesday of Holy Week, for example, he cannot use the collect for confirmation because that particular weekday ranks higher on the table than the ritual Mass does. But inserting an intercession into the eucharistic prayer does no harm to the Mass of the day. In fact, it echoes the meaning of the sacrament celebrated within the same liturgy.
Those intercessions appear in the Ritual Mass because there’s nowhere else to put them. In my view, they do not endure the same restrictions as the presidential prayers.