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.
Catholic Sensibility 
From the citation to St Ambrose’s Hexamaron (commentary on the six days of creation, apparently from Holy Week AD 387):
(23) Why need I enumerate the islands, which often
adorn the sea with their jewelled necklaces? Men who hide
themselves there seek to escape from the world with all its
inducements to intemperate living with a firm purpose to live
in continence and thereby avoid the dubious conflicts of this
life. The sea, then, is a hiding-place for the temperate,
an abode for those who wish to practice continence, a refuge
for those in distress, a haven for the secure, a place of tran-
quillity for the unworldy and a place in this world for the
prudent and moderate. Moreover, it provides an incentive to
devout living for the faithful, so that they may rival the
gentle sound of lapping waters with the songs of the psalms.
Thus, the islands voice their approval with their tranquil
chorus of blessed waters and with the singing of pious hymns
resound.
How is it possible for me to comprehend all the beauty
of the sea a beauty beheld by the Creator? Why say more?
What else is that melodic sound of the waves if not the
melody of the people? Hence, the sea is often well compared
to a church which ‘disgorges a tide through all its vestibules
at the first array of the approaching congregation; then, as
the whole people unite in prayer, there is a hiss of receding
waves; the echo of the psalms when sung in responsive
harmony by men and women, maidens and children is like
the sound of breaking waves. Wherefore, what need I say of
this water other than it washes away sin and that the
salutary breath of the Holy Spirit is found in it? “
Copied (with one spelling correction) from:http://archive.org/stream/fathersofthechur027571mbp/fathersofthechur027571mbp_djvu.txt
“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.”
By what criteria can one measure the ennobling of the intent of the songwriter or composer, Todd? Your sentiments regarding congregational singing taking precendence over choral performance (in the meaner sense of the word) are well-known, but the lack of specificity in your statement, made worse by the coedicil of “even the clumsiest attempts,” renders those sentiments innocuous.
Do you really believe, subjectively, that Carey Landry’s “Abba, Father” taken up by any congregation in any percentage of actual full participation represents a “higher intent” than does a competent, nee beautiful choral rendition of Allegri’s “Miserere?” If yes, one of us dwells in an alternative universe. And were those two pieces paired in a liturgy (yeah, I know), I wouldn’t take a poll, were I you, of which elevated the souls of the gathered faithful more acutely.
Well, Charles, Allegri’s Miserere is a liturgical piece. But as much as I like some portions of Bernstein’s Mass, I have to concede that yes, “Abba Father” sung by a congregation hits the nail more fruitfully and effectively.
And I’ll confess: if either you or I were to put our full arranging efforts into a sung version of “Abba Father,” you know darn well that our musical resources could pull off things quite nicely enough to make it a close call.
That said, Marty Haugen’s “Be Merciful” is a better liturgical setting of Psalm 51. As much as I love your cited classic.