(1) The Office Hymn is an integral part of the Western Divine Office. The Office loses something of its integrity without it.
(2) Just singing any old hymn in the Office doesn't make it an Office Hymn. There is a place in Christian devotion for 'affectionate' hymns - I rather like Fr Faber's, for example. But the old Office Hymns are sober, elegant, dignified, biblical, patristic, corporate rather than personal, in the old tradition of the Roman Rite.
(3) If you can't say/sing them in Latin, the best English translations are those by the Anglican Catholic Fr J M Neale (a lot of which you will find in the English Hymnal: not the New English Hymnal which may have excellences but makes no attempt to provide a full set of Office Hymns). I say this, not simply out of loyalty to one of the great, heroic, persecuted figures of Catholic Anglican history, but for a precise and historical reason.
(4) What Neale translated was the text of the hymns in the old English Sarum Office Book. And that text was pretty well the same as the original text. It was also identical to the text in the Breviary of that magnificent pontiff, Pius V. BUT in the 1630s, Urban VIII, who loved the pagan Roman poets, had these ancient Christian texts mutilated so that they would look like something by Horace in metre, grammar, and vocabulary. They stayed like this until Vatican II, in one of its wise decisions, ordered that the ancient original texts, only lightly revised, should be restored to use. This was accordingly done in the post-conciliar Liturgia Horarum. So Neale's translations are closer both to the originals and to what the Western Church now orders than are the translations made in the nineteenth century by RC translators.
Sometimes people ask what the Anglican Patrimony is. And there is sometimes an assumption that it is something largely irrelevant to many people ... Choral Evensong, for example. I believe it is something that can contribute to the mending and the wholeness of the entire Latin Church. A few weeks ago I had occasion to be with 60/70 priests who were saying/singing the Office together. They, each of them, had the English version of the Liturgia Horarum before them; I have never wasted good drinking money procuring this publication. As I followed the Office in my Latin LH I was surprised to find that the the hymn they were using was quite simply not the one in the Latin Editio Typica (neither were the preces). One simple ingredient I, personally, would insert into any preliminary set of liturgical regulations for an Ordinariate would be the facultas to use the Office Hymns provided in the English Hymnal in connection with the vernacular LH.
Actually, come to think about it: the LH Preces are that part of the revised Office which has worn least well. Some of them positively reek of the Sixties. Would there be a problem about an Ordinariate allowing the Prayer Book Preces to be used optionally? The Instructio Generalis Paragraph 184 already permits local hierarchies to allow alternative forms of the Preces; one would just have to add to Dr Cranmer's Suffrages a petition for the Departed at Vespers.