It rightly has been pointed out that the cappa magna is not a liturgical garment. It was never outlawed outright by Vatican II or any post-Vatican II mandate, but it did fall into disuse for bishops in the New Order of the Mass. It remains as a part of the rubrics for a Pontifical Solemn Sung Mass in the Extraordinary Form of the Mass.
The actual law addressing the post Vatican II usage is:
It is now rarely used, since the 1969 Instruction on the Dress, Titles and Coats-of-arms of Cardinals, Bishops and Lesser Prelates lays down that:
The cappa magna, always without ermine, is no longer obligatory; it can be used only outside of Rome, in circumstances of very special solemnity. (§ 12)
However, the Latin Patriarch of Jerusalem still uses the ermine-lined winter cappa, because he is bound by the complex and unalterable rules of the status quo, an 1852 Ottoman firman which regulates the delicate relations between the various religious groups which care for the religious sites in the Holy Land. This anomaly is most evident at the Midnight Mass on Christmas Eve in Bethlehem. The cappa magna is also still used among groups using the Tridentine Mass.
However, liturgical garb of the post-Vatican II "spirit" of Vatican II variety still looms out there and no progressives ever blink an eye at it. In fact they encourage it because, well, it is so progressive.
So look at the non-liturgical vesture and the liturgical one and tell me which one is more likely to be seen for the complete celebration of the Mass rather than just at the beginning and the end. Again, of the two, which would you axe?