Aram said:
Who says he didn't, and that they just didn't come back?
This seems reasonable, given that at the time you had both the Kingdom of Armenia and the Kingdom of Cilicia; these were no mere vassals, although they were allies of the Byzantines and comprised a buffer zone against invasions from the East.
Also, it is difficult to imagine a scenario where the legates sent to Holy Etchmiadzin would have had a materially different experience than those sent to Hagia Sophia, since we are in both cases talking about the two grandest cathedrals of Antiochene Christianity still extant in 1,000 AD (and the two cathedrals are about the same age, too). Later we of course lost Hagia Sophia to the Muslims, but we have some truly exquisite Orthodox cathedrals that provide a similiar experience, including a newly built cathedral in Kronstadt which is a partial architectural replica of Hagia Sophia.
If I were to make a list of cathedrals currently in Orthodox hands where one could forget whether one was in heaven or on Earth, I would include the Holy Sepulchre, Holy Etchmiadzin, the rock hewn churches of Lalibela, St. Basil’s and the Kremlin churches in Moscow, St. Andrew’s in Kiev, the new main cathedral in Georgia (Holy Trinity, I think), and St. Alexander Nevsky in Sophia, among others.