It is a prayer; that is not the issue. Do some prayers then trump others? Should the 9th Ode of the Canon be stopped so everyone can join in the exultation of "Christ is Risen?"
If the congregation was singing the 9th ode of the canon, no. If the congregation stands there like a bunch of mutes while a few people at a chanters' stand are singing the 9th ode of the canon, their response to the greeting might just be what keeps them engaged in the worship. If chanters can't ignore that and continue chanting, maybe the problem is with them. Priests and deacons are constantly praying one thing while chanters/choir are singing something else and while the congregation is chit-chatting, quieting noisy children, etc. They have to learn to ignore what other people are doing so they can focus on doing what they're supposed to do. What makes chanters special? It's not easy, but it's part of the job.
This isn't about poo-pooing "Christ is Risen" as it is said/chanted many times during hte Liturgy, where there is a place for it. Why is it considered bad for Liturgy to proceed in good order so that the people would be edified. I'm not saying you advocate for some sort of free-for-all during Liturgy, but I fail to see how the order and dignity of the Holy Liturgy be maintained with random shouts of the Paschal Liturgy during the chanting/praying of the hymns.
I grew up without this practice, and my exposure to it has been very limited. I always find it a little distracting, and if it were up to me, I wouldn't do it. But I can appreciate how it "works" in other traditions.
You named two or three moments in a ~3hr service in which these "random shouts" take place. The moments themselves amount to no more than twenty minutes of that hours long service, and I highly doubt that the priest and people are constantly shouting "Christ is risen, truly he is risen!!" for each of those twenty minutes. Are you sure this is really the problem you think it is?
And, by the way, I stand by my comment about people being musically illiterate. They are. that is no delusion. People don't know the difference between a major and minor scale so how the hell do you expect them to be able to chant in the modal system which is almost a foreign musical language to their ears?
If the modal system has managed to hijack the prayer of the whole Church from the whole Church
and turn it into some sort of off-Broadway musical performed by specialists, maybe we need to rethink the modal system.
Of course, I don't think that's the proper solution, but that's the proper logic.
IF people want to learn, great; I'm all for that. But most people don't and believe they have every right to sing even if it's totally off. That IS distraction.
God can handle it. And the Liturgy is for God in the first place.
The people have the right to sing. Actually, they have the obligation to sing in the sense that they have the obligation to pray what's being prayed so that they can exercise their baptismal priesthood. They're not just a bunch of candle-lighting icon smoochers who we need to keep around in order to pay the bills.
Why is a demand for good order somehow considered anathema? I've had bishops stop chanters when they were chanting in the wrong modes or just chanting poorly. Would you reprimand them? Why is good order all of a sudden a bogeyman to be feared?
I wouldn't reprimand the bishop in that case because it's the job of chanters to chant well. But if a bishop stopped the congregation from singing because he didn't think they sounded good enough, yes, I would be more likely to criticise that. I would want more details, obviously, but I find that to be a bigger problem than insisting that chanters know how to chant. I expect a priest to know how to celebrate the Liturgy and I expect chanters/choirs to know how to sing well. I've seen enough sloppiness from both priests and chanters to give most congregations a pass when it comes to their lack of Capella Romana quality singing.