As I wrote in a posting that got deleted from YC.com (because I had been banned before, was posting using a pen name and Denise remembered it was the name of a dead person), there is nothing wrong with devotions to the Sacrament outside of the Mass/Liturgy, but such never evolved in the East because there were no heresies against the Blessed Sacrament there, even among the groups once thought to be heretical (Orientals and Assyrians, formerly called Monophysites and Nestorians), against which to react.
There is no theological reason not to have holy hours and Benediction in the East but there is no historical reason and therefore no liturgical reason to do so, as Bishop Kallistos (Ware) has written.
There is a necessary tension in orthodoxy, a balance, between this natural outpouring of devotion and the overarching belief that, as the admittedly Protestant Articles of Religion of the Church of England put it, the Sacrament was not instituted mainly to be carried about, lifted up or worshipped, but to be used as food and drink. Something the Christian East has retained without the negation in Protestantism.
Eucharistic belief on both sides is the same, which is why in the Byzantine Rite there IS 'Benediction' but, true to the original use of the Sacrament, DURING Liturgy, after Communion, not outside it.
A push-button monstrance may be tacky but it's orthodox.
The perpetual-adoration craze among some well-meaning conservative Catholics isn't traditional. Traditionally such use of the Sacrament was strictly regulated (and included things like the Forty Hours' Devotion once a year) - technically one needed the bishop's permission to have Benediction, and perpetual adoration was only done by some contemplative orders of monks and nuns. It is an understandable reaction to the trashing of the Mass.
But the solution is not to take a practice that has its place but rightly belongs on the periphery of the Eucharist and move it front and center, but to restore the objective, Godward character of the Mass itself (shorthand - eastward position and no lay distribution of Communion) and to promote the use of the office (hours) over nonliturgical devotions - a lot like in Orthodoxy.
Something neither the liberals responsible for trashing the Mass nor the perpetual-adoration craze seem to want to hear.