You're asking this question with the mindset that we aren't already in the Messianic Age. The Messianic Age relates to the idea that the world is changing in such a way that we are ready to accept the Mashiach once he has arrived. It isn't simply an age marked by "He's not here/He's here."
In fact, every generation is believed to have an individual who meets all of the characteristics of being the Mashiach. The revelation hasn't occurred yet because the revelation requires the world to be ready for him.
The Mashiach doesn't reveal himself until we've met our part of the prophecy as well. It's a partnership rather than a one-sided affair. It is said that if the vast majority of the Jewish nation all repented for their sins overnight, the Mashiach would be revealed to us.
R. Aha in the name of R. Tanhum b. R. Hiyya, "If Israel repents for
one day, forthwith the son of David will come." - The Jerusalem Talmud
Judaism is a religion of process. Things rarely occur within singular events and instead occur over a process over time.
- The world was created in 7 days
- The world was flooded for 40 days and nights
- Exodus occurred over a year with Ten Plagues (Talmud - Ediyos 2:10)
- The Jews wandered the desert for 40 years before we were ready
There is a very clear theme that runs through the Torah and this theme is things don't occur within an instant. Process is a function of divinity and things don't necessarily happen overnight and in singular events.
The problem with your question is you're thinking of the Messianic Age as a thing which occurs overnight or in an instant. In reality, we're discussing something that is a process which occurs over decades or even centuries.
The Jewish refugees and Holocaust survivors who came to Israel after WW2 was one level of process.
The Jews leaving the neighboring territories of the Middle East en mass was another level of the process.
The continual arrival of Jews through Aliya is another level of process.
Again, the Torah shows us that things rarely occur in singular events but are processes that occur over time. To believe that because most of the Jews left the nations you cited is evidence that the prophecy can't be fulfilled is simply ignoring what is occurring as we speak.
A good analogy for the Messianic Age is to think of it as a pregnancy.
The average pregnancy takes nine months to complete and as the pregnancy draws closer, the mother experiences further discomfort and the tremblings (contractions) of a coming birth.
We're currently experiencing the contractions of the Messianic Age. The fact that birthing this new world can take some time, that doesn't mean it isn't happening. We need to be patient and accept that the process is moving forward at a natural pace.