The Dalai lama certainly did never refer to himself as the "Pope of Buddhism", the Dalai Lama alwasy refers to himself as a monk.
The "self-promotion" that has been going on for decades over the figure of the Dalai lama is nothing else but a motion of his vows to benefit others.
In fact, in instauring the ban on Dorje Shugden and even contradicting himself in his speech sveral times over the matter, he is even looking like a "fool" to some, but that does not bother Him, in fact, that also is a motion of his vows to benefit others, even if one has to loose his reputation in the process.
There are many more things said about the motivation for the Dalai Lama to promote himself, or even instaure the ban, it was said that he wanted to unite and control all sects... Maybe it is so, maybe it is not, I don't know. But what I know is that the Dalai Lama does not act in these ways to gain control for himself, for his own gain, no! the Dalai lama has worked tirelessly to bring people back ontio their spiritual path, and for that, he has gain recognition, he has promoted himself, and he also instigated his own "reputation loss' with the ban on Dorje Shugden.
On the same ground, the Dalai Lama has made choices that were debated or challenged, some choices that did upset such or such group. People operating at that level will always have to go through that, there is no exception. It does not mean that I agree with the Dalai Lama, I am just sharing here what I think about the situation, and I also do not claim that I am right.
If people see him as the Pope of Buddhism, it is because perhaps he has worked very hard to promote Buddhism, to a point where he became one of the most famous monk in history. It does not mean that he claims for that title, it does not mean he "enjoys" that fame.