I can see Roman Catholics doing this, because we can see that many who post at CAF are clamoring for a chance at receiving communion in Orthodox temples. Some are genuinely hurt when they learn there is no offer to commune.
Sorry for the delayed response.
I agree. I also think it is not material which side initiates the drawing closer. While some Catholics may be hurt at being refused communion, it will eventually serve to remind them of the nature of the eucharist, which may not really be strengthened by too much reception.
The cat is already out of the bag to a degree. There are Orthodox who have basically permitted entire Episcopalian communities into the fold. The “Antiochean” Church comes to mind. Those are the Orthodox who are most likely to attend a reconstituted traditional Latin mass. From there, the thing spreads. But you are correct certainly - most individuals will be Latins going East, and that is related to the comment you made about why Orthodox tend not to go west, though this may change in English speaking countries over the course of the next generation. It may also change in Russia, depending on whether the episcopate acts courageously on moral issues facing the west.
When we attend each other’s services over time (I am not speaking from experience), I believe that we begin to see theology and Church from a new perpective, which we compare with and evaluate against what we came in with. We harmonize insofar as possible, distinguish real from apparent contradictions, and re-evaluate what seemed settled. Invariably, this entails change. Equally invariably, it does not entail as much change as we expected.
That is just how the human mind functions. Because people are social, those who have connections to both worlds act as a kind of bridge.
It is not accidental that schism happened at a point in time when Christianity was a rising force in the world. Entire new lands and peoples were becoming Christian, which offset the losses inflicted by Islam. At the time, the decision was not final with Islam anyway, and it seemed that the tide of that challenge might be receding. Many in North Africa and the east were still Christian, also.
Schism was a luxury that Christendom could afford.
The process is now running in reverse. That is why unity will occur.
Either that, or we will all need to ask the Turks very kindly for the use of their caves.