I understand that. But my point is that such an attitude is problematic. Its ok for us to share traditions with one another if they enrich our experience of our Lord Jesus Christ. I certainly believe that Eucharistic Adoration is one of those things that all sui juri Churches, regardless of their particular traditions, should take part in.
Why? The Catholic Churches of the Byzantine Rite are not places for the Latins to come in and "feel good" because the priest faces east and uses incense. They reflect a totally different small tradition and our people have been put through a lot by the Latins since the 1500-1600's. The development of Euhcaristic Adoration was a direct result of the local Roman Council of Lyons, to make the new declaration of transubstation "Lex Orandi Lex Credendi." Before the council of Lyons, the priest only had one elevation of the Holy Gifts ( like the Orthodox/?Byzantine Catholics). In the local council of Lyons, it was changed to the two elevations still present in the 1970 Roman Catholic missal. That being the elevation of the Blood and a seperate elevation of the Body, with the third elevation consisting of both Species. It developed into a practise to go from church to church to witness the elevation, even in England with the people shouting for the priest to hold the Eucharist higher.
Note, the fact that it is said that the reason the altar boys hold the back of the priests vestments when he is facing East in the Latin church is because it is said that the heavy vestments were a burden in the middle ages because the priest would hold the Eucharist up for extended periods of time so the faithful could adore the Eucharist (the highlight of the Mass which was said mostly quietly by the Priest, it let the faithful know what was happening and since frequent reception of Communion in the Orthodox and Roman Catholic Churches wasn't prevelant until quite recently). People had come to seperate themselves from partaking in Communion and participating in adoration, and the public service of the specific practice of Eucharistic Adoration was instituted to bolster the proclamations of the local Council of Lyons.
Anyway, so exactly then why should we adopt Eucharistic Adoration?
When we celebratea Liturgical Service ( Greek, Liturgica, work of the people) which includes Matins, Vespers, Compline, Akathists, Paraklesis, Parastas, Panachidas, Lityas, Divine Liturgy... they are communal celebrations, not time for private devotions. Private devotions are something you do on your own time, at home, in preperation for the communal Liturgical services.
So having a community come together and privately praying during a Eucharistic Adoration goes against the grain of the Eastern praxis, not just the Eastern practice but the very definition of Liturgy (liturgica, work of the people, and that term isn't limited to the most special work of the people, the Divine Liturgy, in Roman terms, the Mass).
There is nothing wrong with private Eucharistic Adoration, going into church and conversing with Jesus is a beautiful thing.