Yes, I think that this should be done, but not for the reasons you're probably assuming. I am all in favor of the Catholic Church making its rituals as obscure and inaccessible to the common man as possible. This will have the effect of driving people away from Catholicism, which is a very toxic brand of Christianity.
The Catholic liturgy should not be read in the Gospels' original Greek language in the United States becaues very few people actually know this language. There is no point to reading these scriptures in another language if nobody understand them. Therefore, they should continue to be read in English today.
In order to reach a larger audience, the Bible has been translated for ease of use. This has been an accepted practice among Catholics for more than a Millennium. This was to keep from alienating the poor, barely educated populace. Some people only owned one book, and could barely read that in their native tongue. It is hard enough filling the pews with translated verses. Think of the fallout if they were not only asked to come every Sunday, but also to understand a new language?
Except in areas where most of the congregation speaks and reads Greek, if the liturgy was read in Greek, most people wouldn't be able to follow it. Occasionally it would be a good tradition to follow. While the Catholic liturgy is such that it should be the same anywhere in the world it is celebrated, for the most part it should be in the language of its congregation.
I do not believe Catholic liturgy should be read in the Gospels original Greek language. As the Catholic church gained power of Europe they often used art work to illustrate the stories of the Bible because people were not capable of reading. I believe switching to the Greek language would cause a similar problem in today's society which is totally unnecessary.