The adoration of the Eucharist outside of a liturgical context is a uniquely Roman Catholic and affiliated churches' (e.g., Maronites, for whom it is a Latinization) phenomenon.
It is enough that Christ told His disciples and us "Take, eat of it all of you", and "Take, drink of it all of you". And so we do.
In my personal view (i.e., not from this or that source, since I don't know of any OO sources that address this RC devotion), this is one of those things where the impulse (to affirm Christ in the Eucharist) is good, but somehow along the way it took a turn into a
form that I can neither really understand or find supportable. For one thing, why is this happening in a non-liturgical context, and what does that say about the liturgy as it is in the RCC church that they separate it into its own thing outside of the liturgy, so as to adore Him further?
We prostrate ourselves before the holy and precious body and blood of Christ our Lord in the liturgy, so I guess that would pass for 'adoration' in a Western context (in the sense that they say that this is to show due reverence to the reality of the Eucharist, and this is why we do what we do -- because Christ is truly among us, and when the priest raises the body and blood before the prostrated congregation and proclaims that these are the holy body and precious blood, that's exactly what they are), but here again the form is different enough that such a thing could be comfortably fit into a Coptic Orthodox context, either inside or outside of the liturgy. More basically, I don't think that it is something that anyone would really think to do. Because of what is contained in the liturgies and prayers of the Church, and the way these are lived out, there really isn't any doubt regarding what is going on and why, and to (re-)affirm the reality of the Eucharist would be and is as simple as looking at those liturgies and other prayers.
To that end, a fraction prayer to the Son from the Coptic Liturgy of St. Gregory reads as follows:
Blessed are You, O Christ our God, the Pantocrator, Savior of Your Church. O Logos who can be contemplated and Man that can be seen,
who through Your incomprehensible Incarnation have prepared for us the Bread of heaven this, Your holy Body which is mystical and holy in every way.
You have mixed for us a cup from a true vine, Your unblemished divine side,
which after You had given up the spirit, flowed for us blood and water, and became purification for the whole world.
Acquire us to Yourself, O Good One, we Your undeserving servants.
Make us for Yourself an assembled people, a kingdom, a priesthood, and a holy nation.
Purify us also O our Master, as You have sanctified these gifts set forth, which You have made unseen out of those which are seen and (have made them) Your rational Mysteries, O our Lord, God, and Savior Jesus Christ.
You, because of the multitude of Your compassions, have made us all worthy of sonship through holy Baptism.
You have taught us types of mystical prayer, so that we may entreat Your Father thereby.
You also now, O our Master, make us worthy, that with a pure conscience and good thoughts that befit sons, and with yearning and boldness,
We may dare to cry to God, your holy Father who is in the heavens, and say:
“Our Father ....”
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The contemplation of God the incarnate Logos is an affirmation of the reality of the incarnation (as with the following point, that He is "Man who can be seen"), so while it would be absolutely wrong to treat Christ as not able to be contemplated (as that messes with our theology of the incarnation), I am really not sure what can be gained through Western Eucharistic adoration that is not abundant in prayers and practices described above.
So maybe the question should be reversed:
Why does your church practice Eucharistic adoration, Erose?
