I personally don't care for it, not that Cat's personal opinion matters. But I just want to make sure you realize that not everyone agrees with you that it brings heaven closer to us.
I prefer hymns, both traditional and modern, in my own language, with a regular melody that I can hum as I am working or playing outside of Mass.
But to each his own. I respect your opinion and preference.
You asked the question, "Why don't we hear this more often at Mass?"
The answer is, "Because it's hard to learn unless you have a musical background and a good conductor, and probably a rehearsal accompanist, since so few people read music."
The version that you linked us to is being sung very well by good singers. Honestly now, how do you think that same music would sound sung by the people in your parish? If YOU had to sing it, would YOU sound good, like the people in your link?
My husband and I listened to a CD of Gregorian chant a few weeks ago. His comment was, "Well, if the singers in the church all sound like that, it would be OK. Problem is, the singers in most churches don't sound like that. It would end up sounding like those funny cat videos--meeerwwrowal!"
Now with a good conductor and some good singers who actually have time to do some rehearsing, this Mass would sound OK to those who like this kind of music.