It is certainly no news that office hymns from the chant repertory can be sung as well to latter day harmonised tunes - and vice versa! Both styles of tunes are metrical and are intended for metrical verse hymnody. All one needs do is to match the metres.
As for using Vom Himmel for A solis, why not. Luther, as many probably know, said in response to some of his reformer colleagues, 'why should the devil have all the good tunes'. He said this to those who thought music should be banned from worship. We might add to his observation, 'why should the Protestants have all the good tunes'. Of course, thy don't anyway - the Gregorian tunes are as beautiful as any latter day mensural ones. We are fortunate indeed to have both in our day.
The English Hymnal uses Vom Himmel hoch as the modern tune for its other Christmas office hymn, Christe Redemptor omnium - in translation, Jesu, the Father's Only Son.
There are many tunes that Americans assume are Lutheran that have been in extensive use in the RC Church in German speaking nations. Msgr. Rothensteiner apologizes in one of his collections for items that some might assume were outside the faith. He even used some of Miss Winkworth's translations! Not only music, but texts too!
Even Veni, Creator Spiritus can be sung to Vom Himmel hoch. (and vice versa!), not to mention quite a few others in your pick of languages. And Roborgelmeister is right: all German hymns are not Lutheran. I wonder how may people have seen a German hymn or tune and thought 'oh, that is Lutheran - Catholics mustn't sing that'. Such paranoia even over words that express no heresy, and, may have been penned by a Catholic to start with.
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