Yes, I think the expression "to pray for the intention of the Pope" is not so good, nor so wise. It was introduced in the 19th century when the atmosphere of an exaggerated papacy was at its height. This is not healthy.
I think, in the future, the Church should change this and propose another formula for prayer. Perhaps it would be better to pray for the spiritual well-being of the Roman Church, of which the Pope is the head, and in other ways, but I believe this should be corrected in the future. Some people have scruples and doubts about praying for certain intentions because sometimes Pope Francis publishes intentions that are not Catholic. We cannot pray for such intentions when they are formulated ambiguously.
We can only pray for clear intentions, not ambiguous ones. In this case, to obtain a plenary indulgence, we can simply pray for Pope Francis himself, as he often asks, "Please pray for me." In this case, it is also the Pope’s intention to pray for him, not in his formal intention.
Dear visitors of Gloria Dei and all who have already written or who will write a personal message to me. I am grateful for your attention, your kindness, for your spiritual support and especially for your sacrifices and prayers for me. God may reward you!