I'm one who is beginning to investigate that path. I would offer a few thoughts on why more traditional Catholics don't investigate Orthodoxy. In no particular order:
(1) Tribalism. "I'm Irish/Italian/Polish, etc. Orthodoxy is for Greeks and Russians." The assumption that Orthodoxy is ethnic is definitely a barrier for many.
You can be Orthodox in Italian
just as easily as in Greek or Russian. Though I know what they mean, as the Church expands into areas that have not had Orthodoxy as a viable option for their people for centuries (due to the overwhelming influence of the Catholic or Protestant churches), the basis for this criticism becomes less and less true. There are places in the world today, solidly western places like Bolivia and Guatemala, where newly-planted Orthodox churches of various jurisdictions are made up basically entirely of converts, as well as churches set up in Europe (at least in my communion; I'm not sure that the EO have really gotten around to this) like the British Orthodox Church and the French Coptic Church that exist entirely for the purpose of giving the native Britons and French places in which to be Orthodox and European -- that is to say, to recover their lost Orthodox Christian heritage that has been obscured by the dominant RC narrative.
(2) A perception of moral laxity with respect to divorce and contraception. Such a perception is not fair, obviously, but given Rome's unyielding stance on these issues, it is an issue. Never mind the sophistry of the annulment process...
What seems like moral laxity from the outside is experienced as pastoral wisdom from the inside, in not issuing a "one-size-fits-all" edict against non-abortificent
forms of contraception (abortion is forbidden). The Orthodox Church on a worldwide level is, much like the Roman Catholic Church, a church of many, many poor people in societies that do not have the infrastructure to handle unrestrained population booms. Besides, with the strict fasting schedule kept by many Orthodox, this becomes less of an issue as periods of sexual abstinence are observed.
(3) Orthodoxy = the loss of Latin. Absolutely not, my friend!
Though you're right it is not the liturgical language of any Orthodox church. The Orthodoxy is in the faith, not the language.
It must be remembered that the construction of the "traditional Catholic" identity includes Latin over and against the banal vernaculars most Catholics got in the late 60s/early 70s. It is a marker of identity.
Well, I can't speak for those who like to pretend they are denizens of the Roman empire, but I haven't stopped praying and chanting in Spanish on occasion (sadly not in church, since the demographics of my particular parish wouldn't make it appropriate; others' would, though
I don't really have anything to say about the other reasons you mentioned, since I experienced them myself too in converting from RC to Coptic Orthodox. I mean, it's easy for me to say "Well, don't be afraid of that, because it's not true!", but until you believe it yourself...
Regarding the Hail Mary that forms an integral part of the Rosary (and, incidentally, the only part I ever really felt comfortable praying as a Catholic...hmmm), my priest has said that there is nothing really wrong with it, just that it's not a part of our tradition so I should focus on learning and practicing the traditional prayers of our church (i.e., the Coptic Orthodox Church, for which the Thanksgiving Prayer, the Trisagion, and others are traditional). He never said don't pray it. If I remember correctly, there is even an Eastern Orthodox version of it (I used to know it in Russian, but have forgotten over the years).
But stuff like the Sacred Heart, yeah, that's definitely out. As I recall, none less a foundational figure than St. Basil tells us not to worship parts of the body considered separately, and so we don't. Roman Catholics should listen less to their medieval and later mystics and such and more to the early fathers if they want to understand why they'd have to give some things up, but that said it is again not an abandonment of their cultures and traditions, but a rediscovery.
(Curiously and sadly, you are likely to find the standard RC/Latin image of the "Sacred Heart" in many OO churches and homes, but that is for social and cultural reasons and out of ignorance more than any level of knowledge or acceptance of what that image depicts. I tried explaining it to people at my church over our post-liturgy meal once and they were shocked and thoroughly confused. "Abouna, is this true?! It sounds crazy." Oh, my poor congregation. They just thought "Ah, here is a nice picture of Jesus! We love Jesus!" <Jaws music> Little did they know... </Jaws music>)
Our holy Roman Fathers, St. Arsenius, St. Maximus and St. Domatius, and all who followed their way into the desert and El Baramous Monastery, pray for us.