Superman not only apologized to Lois, he explained to her why he left, and also let her know what his life is like. "I hear everything..." He let Lois understand the responsibility of being Superman and how this responsibility wore on him, but now he realizes that it is indeed his reponsibility.
I understand your problem that Superman wasn't allowed to resolve the issues of fatherhood within the realm of the story.
I also think that in the Donner/ Lester film(s), Superman never treats being Superman as a burden. It becomes a challenge to decide between being super and being human, but he faces it with conviction and honesty. However, to me in SR, the whole "I hear everything bit" seems like he's going for pity from Lois. It also comes off as an excuse for having left, although it doesn't really make sense.
If as you say he's trying to let her know what his life is like, it seems that if they were in a sexual relationship they would have been over all this before. It seems like a real case of putting the cart before the horse in a relationship, and that is just the opposite of the way it was treated in Superman II. In that movie, all is on the table before they become involved. Perhaps, if Singer had been clearer on the context of their relationship before Superman left it would come off better, or at least more distinct without so many unresolved issues. It really seems like he skipped a whole movie before SR that needed to be told to really have a clear understanding of what's going on in SR. Personally, I can't imagine a scenario where Superman would be acting the way he does.
Lastly, I think the situation that SUperman put himself and Lois in is the kind of thing you can never really get redemption for. It is one of those life changing mistakes. A simple apology comes off as hollow and meaningless. "Gee, too bad you couldn't have said that before you left."
I think there are better ways to show Superman's humanity w/o making him the father of a child out of wedlock, an absentee father and an emotional weakling. Those issues of responsibility hurt those he is closest to. At least in Superman II, when he acts irresonsibly he is thinking of Lois. Those aspects of characterization are just polar opposites in my opinion.
Lastly, I don't think Donner's films were perfect or definitive of the character and I was really hoping for a Superman movie rooted more in the comics rather than the Donner films.
To me the biggest thing I would like to see done is have an origin that shows Clark making the decision to be Superman of his own volition with the guidance of his parents. It's been that way in every version of his origin. I've re-read the origins from Superman #1, 1939, Superman #53(I think, it's 1948), Byrne's Man of Steel and Birthright.
This is one aspect that is consistent in all of them. However, Donner has Jor-El as the guiding influence and raison d'etre for Clark being Superman. It works up to a point in Donner's films, but I think Jor-El's mandates also become an artificial conflict that is not necessary when it comes to having Superman choose to be human to be with Lois or stay super powered to be Superman. I know Donner was playing on a Silver Age theme of SUpreman not being in a serious relationship with Lois, but in the comics it was his own decision to do this in order to maintain his effectivenes and keep his focus on his role as Superman, a role he clearly believed to be the responsible and correct thing to do.
I think Singer has tried to extend this theme in SR, but his treatment of if just twists and warps the responsible and wholesome goodness of Superman's character into an unrecognizable 'bizarro' version.