I guess it's worth mentioning that Star Trek has always been a product of its time, and also pretty weird about it. For example, consider two episodes of The Next Generation...
On one hand there's "The Outcast," about a planet of genderless people who lobotomize those born with the "aberration" of wanting to identify as a particular gender. Riker falls in love with one of them, who secretly identifies as a woman, and the whole thing turns into a Prime Directive nightmare (while also being an allegory for gay rights).
On the other hand there's "The Host," the first episode with the trill. Crusher falls in love with a (male) trill ambassador and eventually learns about the symbiotes. The original host dies, and the symbiote is transferred into a trill woman. It ends with Crusher giving a pretty bizarre monologue: "Perhaps it is a human failing, but we are not accustomed to these kinds of changes. I can't keep up. How long will you have this host? What would the next one be? I can't live with that kind of uncertainty. Perhaps, someday, our ability to love won't be so limited."
Not to imply that Crusher must be bisexual, but come on, just say it. Don't turn her heterosexuality into quasi-philosophical rambling.
Getting back to the question of Cochrane and the Companion, I can basically give Cochrane's obliviousness a pass. The Companion was a strange ethereal life form, and one can imagine that the mind meld would still be full of ambiguity. Maybe the better question is, why did the Companion have a human screenwriter's understanding of love, when it was an immortal glitter bomb?
Anyway, probably the biggest rug the plot gets swept under is that the Companion apparently kills the ambassador in order to have a human body with which to make Cochrane fall in love. Now there's a dark ending that isn't dwelt upon.