This question is far less in vogue among world organizers these days, but it was a significant step in 1963:
The Second Ecumenical Sacred Council of the Vatican, recognizing the importance of the wishes expressed by many concerning the assignment of the feast of Easter to a fixed Sunday and concerning an unchanging calendar, having carefully considered the effects which could result from the introduction of a new calendar, declares as follows:
- The Sacred Council would not object if the feast of Easter were assigned to a particular Sunday of the Gregorian Calendar, provided that those whom it may concern, especially the brethren who are not in communion with the Apostolic See, give their assent.
- The sacred Council likewise declares that it does not oppose efforts designed to introduce a perpetual calendar into civil society.
But among the various systems which are being suggested to stabilize a perpetual calendar and to introduce it into civil life, the Church has no objection only in the case of those systems which retain and safeguard a seven-day week with Sunday, without the introduction of any days outside the week, so that the succession of weeks may be left intact, unless there is question of the most serious reasons. Concerning these the Apostolic See shall judge.
I’m not aware of any perpetual calendar plans that didn’t adopt days outside of the week as part of the plan. I’m not sure that the Sabbath notion of rest isn’t more important than a literal string of seven-day weeks. At any rate, I don’t think a perpetual calendar is coming soon. The world has far more contentious issues at hand.
Christian agreement on the date of Easter would seem to be more of a priority. I wonder how far away we are from that.