To be the annoying person who answers a question with a question: is there a good reason the choir doesn't lead it as a group, and sing the verse?

This would be the least of my worries. If a Protestant wants to spend time with Catholics and participate, something good might be happening.

Participation in music like this is a fantastic way to lead to RCIA. I've witnessed it myself many times. I have never hesitated from allowing those in the choir to serve as a cantor (though I too prefer the entire choir to lead the Gospel Acclamation), and being Catholic is not a qualification to join the choir—I don't ask.

Properly speaking, a Protestant can't participate in the Mass at all. I don't mean that he's not allowed, but that he's not capable of doing it, anymore than a man is capable of being pregnant, or a women of being ordained.

Not sure about this. Protestants are not allowed to receive sacraments, but my understanding is that the basis of participation in the liturgy per se is baptism, not orthodoxy, and that non-Catholics are generally welcome to join in prayers and singing at Mass and other Catholic services. As for the choir, as I have written before on this forum, Church documents describe two kinds of choirs or scholae: a strictly liturgical choir, which is all male, and a choir of the faithful, which may be mixed or all-female. An FSSP priest I know has stated his opinion that a valid argument could be made in favor of non-Catholic singers supplementing a weak Catholic choir, in which case the Catholics would constitute the real choir "legally" speaking. To answer the question, I would not have a non-Catholic singing the psalm or alleluia verse alone unless there were some urgent necessity such as the assigned cantor getting sick without a Catholic replacement. In fact, if that were to happen, I would probably sing it myself.

I wouldn't want a non-Catholic to be singing from the sanctuary, except as a reader, acting in accord with the official norms for ecumenism, which allow the occasional admittance of a non-Catholic as reader for a Scripture passage (other than the Gospel). These norms presumably only apply in the modern form of Mass.

Some choirs are harder to get into than others, for sure, but that is often based on ability.

At least in these parts, where the majority of professional church singers are completely irreligious, it has never seemed to be an issue for any one of them to cantor.

Quite a few responses have focused on merely being part of the choir which is not really the gist of CGZ's comments (at least the way I read them). I thought the distinction being made was between singing in the choir (which most certainly can be an outreach) and taking an official role within the Liturgy... which I think is most certainly quite different.

In exceptional cases in the EF, a lay person can be the sub-deacon of a Solemn Mass. Would none of you see an issue with having a Protestant or non-Christian in that role... purely because you see it as ecumenical? Or in the OF, would none of you raise an eyebrow at having a Protestant or non-Christian act as a Eucharistic Minister simply because you think this could be good for the individual in question?

A non-Catholic musician performing a specific MUSICAL role in a Catholic Liturgy is one thing. Performing a LITURGICAL role is quite another. It is not a specious distinction between the two.

A personal observation, rather than a direct answer to the question:
The final "inciting incident" which led to my conversion was when the organist I was dating at the time wished to have me serve as a cantor at his parish (I have a degree in vocal performance) and his priest refused because I was a protestant. I'd already served as a cantor at the local cathedral a couple of times when the boyfriend subbed there, so I was very angry and confused with the priest's decision. Ultimately, I realized that my deep distress over the situation had to do with the larger issue of feeling excluded from liturgical participation and a desire for the Eucharist. Had that priest not held firm to his understanding of the role of a cantor, I might not have come to that realization, which in turn led to a master's degree in sacred music and a full-time job as a music director.

Let's face it, the roles of acolytes, cantors, lectors, etc. have been significantly downgraded. They are not clerics, in fact many of them have no training whatsoever for the roles they are attempting. The problem is not with musicians, but with the leadership of the church - or lack of it.

Interestingly, when I worked for the Christian Church (Disciples of Christ), it wasn't uncommon for adults to be re-baptized multiple times. They looked at it as a kind of renewal, re-commitment, or similar. Different mindset.

But I think that all the LAITY should sign, voluntarily, to shame the clergy into signing.

Too many of the clergy have no shame. Good luck with that!

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It is not suggested in GIRM, or anywhere else AFAIK, that the Acclamation before the Gospel ought to be sung from the ambo. In the most solemn form it accompanies the procession with the book of the Gospels from altar to ambo (GIRM #175 or #133), and singing from the ambo would get in the way. Also the verse/s may be sung by the choir, and the Alleluia is to be sung by the people, leading by a cantor is just one option.
GILM does not list it as suitable for the lectern

#33. Since the lectern is the place from which the ministers proclaim the word of God, it must of its nature be reserved for the readings, the responsorial psalm, and the Easter proclamation (Exsultet) The lectern may rightly be used for the homily and the general intercessions, however, because of their close connection with the entire liturgy of the word. It is better for the commentator, cantor, or director of singing, for example, not to use the lectern.

but what is the practice in Rome? what is going on in the average church?

Let's not go there. Maybe the "average church" has someone at the lectern, which is covered in a rainbow flag. Maybe the priest is wearing a rainbow-coloured stole. Maybe the same person who serves as lector leads an LGBT group, after Mass, on how to make the Church more "accepting" of LGBT or "ecumenical" agendas. Apparently there will even be a "gay pride" "parade" in Rome next month, so...

People keep saying, "while not ideal..."

Well, then... What is the best / ideal practice?
Let's do that, instead of what might be the current or popular practice in Rome or elsewhere.

Yes... so you are saying we must seize power. #Resist. #SeizeThePower. Wait, what forum am I on?