Even though it is a Latinization, why discourage it? The beauties of the Faith should be open to everyone in the Church. I am canonically a Latin, yet I go to the Divine Liturgy of St. John Chrysostom whenever I can, and pray the Jesus Prayer (a Byzantine-ization?) before/during the Tridentine Mass when I go there.
Does a devotion need to be a reaction against a heresy? I am glad that the Orthodox have never denied the Real Presence (and, from my own readings of Orthodox literature, I have never seen it denied - the occasional polemic against the word “transubstantiation” seems to me just an anti-Latin polemic; the doctrine is the same) - but Adoration is a beautiful devotion, and with no equivalent Byzantine practice to do instead, why not add this practice?
Regarding the Rosary, versions of it began as a “substitute” for the Liturgy of the Hours in the West as well as in the East, as a concession to human laxity. Yet it was sanctified by the vision of Our Lady to St. Dominic. Priests and monks today (at least before Vatican II) say the Liturgy of Hours AS WELL AS the Rosary, and this should be the proper state of affairs. For the laity, the Rosary is the primary devotion in the Latin rite, since we are not in a position to chant the Psalms every three hours, but it is pleasing to God for us to say - as many of us do - at least a somewhat laxer version of the Hours (such as Morning Prayer and then Evening Prayer). I see no reason to make it an issue between “East” and “West”; the situation is the same for both of us.
