I don't think the fact that chant propers can be made quite short should be a primary selling point.

It's true they can be brief, especially with something like Fr. Weber's simplified compositions with psalm verses and antiphon repetitions omitted. In those circumstances an entrance or communion chant can be just 20 seconds long. But when done this way they sound insignificant and out of place. They want a fleshed out presence where people can start to understand what's happening musically and meditatively sink into them.

That doesn't imply that it's all-or-nothing, but marketing and performing them as short strange interludes between much beefier metrical hymn singing is in fact awkward as per Reason 2. Rather a choir should try taking one chant - the communion makes sense to me - and give it a serious choral treatment with psalm verses and repetition, and take the temperature from that. It will help in terms of congruence if the priest also chants his parts of the mass.

My only disagreement with the OP is not every weekend Mass, but EVERY Mass

ServiamScores,
Did you get the procession to slow down or do you have a long nave? At my last parish, the nave is very short so we did the proper before the hymn. The bell was rung so people were quiet and listened. It wasn’t ideal but also prevented having the priest stand there awkwardly. It would have been nice to do the hymn BEFORE the entrance procession but that seemed like that would be too difficult to get people used to.

the proper chants are worth the time and effort.

The Rice gradual requires almost NO effort (3-5 notes), and they take 10 seconds. They are a good start for a parish that may be chant-averse or chant-ambivalent. I stressed in our parish newsletter that the propers would not take away our precious hymn-singing. No complaints on that front.

The actual complaining comes from the usual crowd, when the choir's two lengthy anthems replace the offertory and communion hymns, leaving the congregation with just an opening and closing hymn ("but muh sandwich!").

deo27: It's depended on the parish.

My last parish was very "liturgical", so we always had incense, so the introit was chanted during the incensation of the altar. If need be, the priest waited a verse or two before processing in.

At the cathedral, it slightly depends on which priest is celebrant, but in general, they wait one or two verses before processing in. One priest goes in right away, but he has stated explicitly that he doesn't mind standing at the altar during the introit. We have simply normalized it that there is always a hymn and then introit, even if people are just standing listening for a moment.

Depending on the season, I sometimes give simplified introits directly to the people, so they sing the antiphons as well. I've been using the entrance antiphon hymn texts from antiphonrenewal.com, so it creates a really nice synergy when we sing a metrical hymn version, and then things somber-up a little and they sing the chant equivalent which is a more direct setting of the text. Then the two actions reinforce each other.

As for before, four parishes ago that is exactly what we did. We told people to stand, then I chanted the introit, and then the hymn began business as usual. It can work just fine (that was a tiny church).

All that is really necessary is will/support from the priest, and a little catechesis. Tell the parish outright that the antiphons will be chanted, and why. Practical matters on your end can determine whether or not it is before or after. Both work. Just tell people, normalize it, and they will come to expect it.

Proper Chant Resources:

I am struck by the abundance of modern sacred music and by its organization and systematic nature for the liturgy in English. There is nothing similar in Italian and I fear not even in Latin, apart from historical texts, mostly only in Gregorian.

With the exception of funerals, I don’t think it is ideal to completely remove hymns from Mass. If there’s one Mass that should have the full propers sung, in Latin, from the Graduale Romanum. I’ve never been to a funeral where the congregation actually sings, and I’ve been to a lot of funerals in a lot of different places in the last 40 years. I was just listening to the requiem propers on my drive to work yesterday morning and became even more convinced they need to make a regular comeback. I find Catholic English Mass funerals to be too much of an escapism from death, dying, etc. I think we need to learn how to mourn again at funerals.

I think it’s ideal to still start and finish with a strong traditional hymns at Mass on Sundays, as it has become the custom, and singing is just plain good for the soul when it’s something worth singing.

I do think that we need to bring back the propers, especially the full Latin Introit for Lætare Sunday. I feel like it just needs to be there. It’s just not the same.