In addition to /u/koine_lingua's previously cited (and much more exhaustive) post, I'd like to add that some early churches... and, I suppose, the later Church as well... would have a theological uneasiness with Enoch based on its general plot.
It's about a man who's saved from (the conditions that led to) the Flood by being bodily assumed into Heaven and undergoing a kind of divine transformation. Later tradition has it that he himself becomes an angel.
This is a problem with both one strand of Judaic angelology - in which angels are kind of like projections or "individuated portions" of God. For example, in Genesis, the wrestling match between Jacob and the Angel can also be read as between Jacob and God... depending on how literally you want to take the entity's description as "a man" or Jacob's naming the spot "Peni'el"- "God's face"... it's a thing, even for later prophets like Hosea. There's an ambiguity there and in a lot of other references to angels in the Hebrew Bible.
The other issue, though, steps out of the Hebrew Bible and into Christ's uniqueness as the only begotten Son of God, the unique figure who traverses that space dividing Heaven and Earth.
Around the time the canon was being hammered out (around 300 CE), one of the Big Debates had to do with Christ's nature as being part-God and part-Man. Was he wholly divine (a kind of sacred hologram projected on Earth) or wholly mundane (but inspired by the Holy Spirit) or some combination of both, or some kind of overlapping Venn-diagram entity?
One face of this was the Arianism controversy which brought on the Council of Nicea and a bunch of subsequent councils... another, later, phase emerged in the Monophysitism controversy, which eventually saw the Ethiopian Orthodox split off following the Council of Chalcedon.
I haven't read enough into those councils and long-term controversies to know if (or how much) Enoch would have been cited in the debates, but you can kind of see that the story fits a little better with one way of reading scripture than with some other ways. There's this permeable membrane between the human world and Divine reality, and beings can be brought from one state of being into another. This doesn't sit well if your Christology relies on a singular figure who is, mysteriously and miraculously, eternally part of God... not a creature or a creation, but co-existing with God from the beginning of all things.
The Ethiopian Orthodox (part of a group of mmm..mostly North African churches called "Oriental Orthodox" - as opposed to Eastern Orthodox, who are a larger, different group) described themselves as "miaphysite," rather than "monophysite," but still... they hold that there's one person of Christ with one nature. The rest of the folks at Chalcedon said there's one Christ, but he's got a human nature and a godly nature within a single person.
This is some really, really fine hair-splitting, yes.
But it seems to me there's something in Enoch itself that doesn't sit well with the two-natures reading, but seems ok if you can accept Christ as having a nature that's a combination of human and God. After all, Enoch became one with God. He didn't have to be co-eternal to do it.