One has to look at the question of motivation here. If you’re asking why he doesn’t celebrate mass in the Extraordinary Form in order to promote it, you’re answer is in your question. The Pope is not in the business of promoting any form of the mass. SP and UE were not promotions or propaganda for the Extraordinary Form. They were legal clarifications.
In addition, one must look at the language that he uses. He specifically refers to the Tridentine Form as the Extraordinary Form. When he celebrates mass as the pope, it is inappopriate to use a form of the mass that is not the norm for the Latin Church. In SP, he makes it very clear that the norm will remain the Ordinary Form or the Mass of Paul VI.
If we were to ask the pope to celebrate mass in a form other than the Mass of Paul VI, it would be appropriate that he use one of the other “ordinary forms” such as anyone of the Eastern Rites. Those are ordinary to the Church, though they are not to the Latin Church. But when he’s celebrating as pope, he is the universal shepherd and can use any rite he wishes to use.
Here too, the question is how appropriate is it for the pope to use the Eastern Rites, since he himself is a Latin Catholic priest? Obviously, he is not limited to any rite and can use any of them.
The whole thing boils down to appropriateness. The appropriate thing for a pope to do is to use the form of the mass that is the norm for the local church, that would be the Mass of Paul VI. If he were visiting Iraq, it may be appropriate to use one of the Eastern rites. That’s not usually the case. How often does he go to a country where the norm is anything other than the Mass of Paul VI?
Fraternally,
Br. JR, OSF
