I think the Bishop Rome believes that he has been appointed to shepherd (feed the flock) over the whole world, and also has “jurisdiction” over everyone, so even if the jurisdiction is not recognized by the independent community that does not keep it from existing.
True enough, but then certainly the fact that the majority of that world does not recognize his jurisdiction or his role to be as he or your church believe it to be must count for something, right? At least in the context of ecumenical dialogue, if we are to have any.
I mean, my Church calls our Pope “The Judge of the Universe”, but we do not expect nor even particularly care if those outside of us would think this to be the case. It is a particular title, developed in a particular context, with a particular meaning that is not shared by, e.g., Roman Catholics, Protestants, etc.
Sometimes our separated Prostestant brethren are referred to as “rebellious subject of the Roman Pontiff”, since their refusal to submit to his governance does not remove it.
Protestants may be considered differently than Orthodox precisely because they are the spiritual children of the Medieval Roman Catholic Church, as you yourself recognized by writing that their existence is to be laid entirely at the feet of the Roman Patriarch some posts ago. I would think a better example might be made out of Rome’s indelible mark theology, whereby I have had several of my former co-religionists claim that I am still beholden to the Roman Pontiff and am still technically a Roman Catholic in some way, despite having very explicitly rejected all the distinctives involved in claiming that identity some time ago, and again explicitly and very publicly at my baptism into the Orthodox Church in May of 2012. This means nothing to them, of course, because “once a Catholic always a Catholic”, so it does not matter that the Church I am in now holds no such similar view (in other words, if I were to leave the Orthodox Church and repudiate its teachings, as I have done in the case of the Roman Catholic Church, I would not be Orthodox anymore).
We might say similarly (and in fact, we do, if there is reason to) that it does not matter that the Roman Pope believes that he has been given this or that power or jurisdiction. His belief in the reality of those prerogatives (or his entire church’s belief in the reality of the same) do not actually bring them into existence. They are not real (from the Orthodox point of view) just because you have built an ecclesiology around them that seems to require them in order for the church to function as your communion has claimed that Jesus Christ willed it to function. The RCC is quite simply mistaken in these notions, as RCs hold that we are likewise mistaken in not holding to them, as they wrongly claim that the whole church once did.
If there is a way that this obstacle may be overcome, it is probably not to be found by simply reiterating our respective positions and saying “Just because yon don’t see things as we do doesn’t mean that we are not in fact right.” (If you meant something else by stating “even if the jurisdiction is not recognized by the independent community that does not keep it from existing”, then I apologize and welcome correction; I am at a loss as to how else to interpret those words, however.)
We are all fighting over different interpretations of the same history. In that I am glad that I have quite literally far less to fight over with either of you than the two communions mentioned in the OP have to fight over with each other.

(Read: If you think that things like Universal Jurisdiction et al. seem patently wrong to the Byzantines when drawing on the first 1000 years of shared ecclesiastical history with the Latins, just imagine how absurd they must seem to those whose cut-off line in terms of shared history to examine ends some 600 years before that. You can point to Leo I or later Popes, and many later developments that do in their own way point to a centralization of power and governance of the Roman Catholic Pope
in the West, and we will sit here, like the Biz Markie of apostolic Christianity, scratching our beards and saying “Yes, fine, but what does that have to do with us?”

So it is a somewhat daring and at the same time quite reasonable suggestion, which I have heard from several Byzantine friends on these very boards, that Roman Catholics and sometimes also their own leaders are focused on
the wrong schism, at least if they’re more interested in results than photographs…but I digress…and often…)