The issue of musical instruments within the liturgy has always been an unsettled one, and not only in the Church of Christ. The question for Catholics is not the mandate of Scripture or the imitation of the apostolic Church, as it is for the Church of Christ, but that of the function of liturgy and the threat of theatricality.
Even the organ...yes, even the organ. The organ, supposedly one side the Liturgical Musical Wars, cannot rest so easily. For the organ is just as prone to misuse as any other musical instrument within liturgy - perhaps even more so, given the temptation to perform and embellish.
Organ-playing can be helpful, as any accompaniment is, in setting pitch and keeping tempo. But in the setting of the Catholic Mass, the organ can,simply, overwhelm the human voice, both of a schola and of a congregation. Moreover, in the hands - or under the fingers and feet - of an organist who doesn't quite get or respect the organic nature of Catholic liturgy, the organ can be disruptive. In one parish I know of, every Mass part is preceded by a multi-measure, loud, organ introduction, at times composed of the entire piece that is about to be sung - the Eucharistic Acclamation, for example.
I know what she is talking about, and I'm guessing that you do too. This type of approach to organ has damaged the reputation of a great and glorious instrument. I think, however, that there is an answer here, and it isn't to reduce the role of the organ so much as clarify it, and, in some respects, expand it.
My claim is this: the organ is best as a solo instrument, not as an accompanist for singing. (Addition in light of comment below: I'm not speaking here of Masses written for organ and choirs, e.g. Durufle or orchestral reductions.)
Maybe you have heard the way organ and a cappella chant relate to each other in recordings. The organ begins the introit with an improvisation on the chant. It stops and the singing begins. The singing ends and organ picks up again. The textural difference is dramatic and riveting. The human voice and the organ are similar enough to make them integrate and different enough to provide a tantalizing contrast. It is a wonderful thing to hear. It inspires both singers and organists. Same with communion. And offertory. An organ piece on its own is a complete thrill during recession or preludes or other times.
It's my own view that the organ should not accompany chant, and ought to be used mainly if not exclusively as a solo instrument (again, with the organ Mass excepted). The allows the organ to achieve everything it was meant to achieve without muddying up the human voice.
It's beyond me why this approach is not more common but I think it has something to do with the exaggerated role of the organ as a "support" for singing. In fact, the most common result is the organ displaces singing. The strongest singing, over the run, develops when people can hear themselves and when the congregation and schola are put in a position to truly be the music. When people stop singing, the music stops.
I know that the comment box is going to fill with protests that hymns and chant can be accompanied tastefully etc. etc. But I'm speaking of general tendencies that I've seen too often in Catholic liturgy: the example of which Amy speaks, i.e. typical parish praxis. Please consider my thoughts in light of experience that seems to be pervasive. Let the people sing. Let the scholas sing. And let the organists play and play. But not all at the same time.