(By the way, he does no such thing in Superman 3, I just checked).
You talk about how the new 52 removed the traditionnal reasons for him to worry Thing is, by the time the reasons disapear, she's with another man. This Clark is one that missed the coach. She may not find Clark unappealing, but nowhere it is even hinted, appart from a Superman fantasy in AC 12, that she has any kind of romantic attraction towards him. Why would he complicate things for her for no reasons?
Besides, he just don't have to open up. Superman is his secret garden, his "Fortress of Solitude" as post crisis would put it. His little place of solace. We all have this kind of little thing that is "our" thing, and that only our most trusted ones know about. That doesn't make him cowardly, that makes him secretive. Which just is his goddamn choice. Like it or not, he doesn't have to open up to Lois, just like he doesn't have to open up to Jimmy, or Perry, or Aquaman. That doesn't make him cowardly, or selfish, or lacking "deep emotionnal connections" That makes him someone who likes having his own personnal space he doesn't share easily. Which is coherent with someone who would have a secret lair in freakin North Pole.