Seen it before. good site.
Adoration of the blessed sacrament is not a part of traditional Byzantine Rite praxis. It arose in the west due to differences in both praxis and theology, and it can give a focus on the presence of Christ to some who need that.
But, by byzantine theological approaches, one is just as easily able to venerate Christ and be in his presence simply by use of an Icon, as a properly written icon is a window into heaven.
Also, in the construction of Byzantine worship structures, one must also remember that the altar-table is not visible except during liturgies… and not even throughout the Divine Liturgy in many uses of the Liturgies of St. James, St Basil, and St. John; the royal doors get closed during the anaphora in many particular church’s rubrics for the divine liturgies. The Royal Doors of the iconostas block the view of the altar-table, and of the tabernacle upon it. Personal adoration of the tabernacle is thus not readily available.
Further, the eastern churches tend to use leavened bread; the precious body is not in a form convinient to display for public adoration, either.
The combination of the lack of need, with the lack of convinince, has prevented the theology for adoration (save for during communion) from developing.
It is not seen as “effective” or “ineffective” but as simply “foreign and unneeded”.