St Pius X would agree with you. but in practice,it's better for parishioners to worship the singing in the church rather than in the opera house (or some worse places, like in a circus)

No Divas Allowed At Mass!

Also agree: let us hear some examples.

I sought out Responde y Aclama performances on YouTube, even including this week's psalm, and i heard various things. I heard some untrained and some rather trained singing, but nothing I would call operatic. (Aside: I saw a quite a bit of hand-waving suggesting “sing now, this is the response”, which I think is inappropriate: but not operatic as such.)

What do you mean by "operatic style"? Do you mean "A voice capable of being heard without amplification? Or "a voice with a noticeable vibrato"? Or "a performance with interpolated cadenzas and high notes"? I'd say the latter is inappropriate for psalmody (and for the Star Spangled Banner). As for the others, I would prefer to hear a cantor with a solid vocal technique, which means there will naturally be some vibrato. I'd prefer somebody more suited to Lieder than the stage, but I'm not fussy.

Once, I would have said,"That's the nice thing about being a music director; you can have it the way you want it." But that's before I became a music director.