I have mixed feelings about the "Western Rite" as it now stands, though in principle the rehabilitation of historically "western forms" of Christianity is not in and of itself objectionable.
If you read the writings of important 19th century Western-Rite advocates like Dr.John Overbeck (a convert to Orthodoxy from Roman Catholicism), it becomes pretty clear that what they were advocating was an attempt to (as close as possible) revive the rituals of the pre-schism Latin Church. Though there were certainly big supporters of this idea in the Russian Church, very little actually ever came of it. For example, many Western-Riters speak of the "Liturgy of St.Tikhon", which is basically a "corrected" version of the Anglican liturgy of the eucharist. A few things are ommitted, a few other things added (namely, an explicit epiklesis in it's anaphora), and that is pretty much all that it is. Yet what is very clear is that this proposed text and others like it (like a similarly revised from of the Tridentine Mass of Roman Catholicism) were understood by the likes of St.Tikhon and Overbeck to be provisional - for the actual revival of something continuous with pre-schism Western Orthodoxy would require something much more extensive and carefully considered.
Thus insofar as the modern Western-Rite would be considered a "work in progress", it may have some promise.
My big concern at this point though, is that there appear to be supporters within the Western-Rite movement, who have abandoned the mindset of the likes of St.Tikhon or Dr.Overbeck, and basically see the Western-Rite (though they'd never put it this way) as a kind of "corrective reverse-Uniatism"; get rid of the glaring, obvious problems in later western liturgics, but ignore the fact that most of the liturgical developments subsequent to Rome's self-isolation from Orthodox Christendom are to varying degrees founded upon either their loss of the "Orthodox mindset" or as reactions to controversies which simply do not pose a challenge to the holistic faith/praxis maintained by "the East" (which is the genuine, continuing part of the Church of Christ.)
As for "westernizing" Orthodox missions in the west, in the legitimate sense this kind of inculturation has already began (though we need more of it!) For example, there is nothing wrong with converting all liturgical services into careful vernacular, emphasizing the cult of Orthodox Saints native to western soil (whether from before the schism, or more modern Saints who lived in the west like Sts.Herman, Tikhon, John of San Francisco, etc.) There is also no reason why the same East-Roman/"Byzantine" services which became inculturated amongst the various Slavic peoples, could not do the same here, even to the point (with time) of giving birth to different usages and disciplines (which one observes in the rest of the normative Orthodox world.) The Orthodox Church is "traditional" - but genuine tradition has never been static, not in the time of the ancient Fathers (who made some very striking revisions of the liturgics they'd received when they felt it would be pastorally advantageous), nor in subsequent eras.