Pope Pius XII gives Malachi 1:11 as a citation of a universal priesthood. There is a larger context in Malachi 1:6-2:9 that criticizes those who offer something less than their best. Can we bring this wider context into liturgy? Maybe Pope Pius didn’t intend that, but I think it might be apt. Let’s read first:
2. But what is more, the divine Redeemer has so willed it that the priestly life begun with the supplication and sacrifice of His mortal body should continue without intermission down the ages in His Mystical Body which is the Church. That is why He established a visible priesthood to offer everywhere the clean oblation [Cf. Mal 1:11] which would enable (people) from East to West, freed from the shackles of sin, to offer God that unconstrained and voluntary homage which their conscience dictates.
Christ has freed all believers, of course. Does this grace urge us to offer our very best? In the context of 1947, do quiet Masses, silent Masses, perfunctory celebrations fit what God criticizes in Malachi 1:13?
If that takes the text of MD 2 too far, we can still interpret it as an affirmation of long Catholic practice of taking the sacrifice of the Cross and continuing this expression through a cultic priesthood. But a full reading of the prophet reveals a not-so-minor caution on our intent behind the sacrifice.
If you wish, you can reference Mediator Dei on the Vatican web site.