The modern music Pope Pius XII speaks of in MD 193 includes material composed for purposes outside of liturgy: the concert stage, opera, musical theater, and such. It might also have included music composed for non-Catholic worship.
193. It cannot be said that modem music and singing should be entirely excluded from Catholic worship. For, if they are not profane nor unbecoming to the sacredness of the place and function, and do not spring from a desire of achieving extraordinary and unusual effects, then our churches must admit them since they can contribute in no small way to the splendor of the sacred ceremonies, can lift the mind to higher things and foster true devotion of soul.
Even the clumsiest attempts to put together a melody with a few chords for the assembly has an intent somewhat higher than even the most skilled composition for choir. That certainly reads as possible in this section. Pope Pius doesn’t speak here of beauty or quality–though I would certainly assume it for him as well as repertoire choices in a parish. Any piece “becoming” of sacredness and with a liturgical function is potentially, if not probably appropriate.
An actively singing congregation is to be “promoted with care.”
194. We also exhort you, Venerable Brethren, to promote with care congregational singing, and to see to its accurate execution with all due dignity, since it easily stirs up and arouses the faith and piety of large gatherings of the faithful. Let the full harmonious singing of our people rise to heaven like the bursting of a thunderous sea[Saint Ambrose, Hexameron, 3:5, 23] and let them testify by the melody of their song to the unity of their hearts and minds[Cf. Acts 4:32], as becomes (sisters and) brothers and the children of the same Father.
Singing is not just there to usurp the professionals. It is meant to be a testimony of faith on the part of the assembly.