This is such a good point! And for me, it ties into a broader interpretation of their characters: they both mirror each other in being Not As They Seem. Despite their superficial characteristics being complete opposites, they connect because they have a surprising amount in common. And that's because they both contain dualities.
I firmly believe that Bruce is a romantic. Yes, he's often cold and calculating in his relationships, but that's never for lack of caring. In fact, if anything he cares too much: fiercely, pathologically. He cares about Gotham so much that he practically tortures himself in the name of protecting it. He cares about people so much that he's sworn never to kill, even criminals who've caused him immense and personal suffering, because he believes everyone deserves a second chance. He cares about his family so much that he will blow up his own relationships with them if he can convince himself its for their sake. In Batman: The Knight, Bruce tries to get rid of his love so he can be more efficient, more unfeeling, but in the end its his love that becomes his true strength.
Is any of this healthy? No, not really! He's deeply emotionally repressed and can't express any of these feelings in healthy ways. But the feeling is there. And I think in love he can be reckless and impulsive, when the feeling overwhelms him. Thus the proposal to Selina; thus his many entanglements with his rogues, especially Talia, which are pretty obviously Bad Ideas from a logical standpoint. But he loves, and sometimes he can't hold that back.
Meanwhile, Clark also loves deeply, but his love drives him in a different, nearly opposite way. Clark is warm and friendly, raised by emotionally supportive parents - but he's fundamentally not human. He's always kept the alien parts of himself hidden to keep himself and his family safe, keeping his powers under careful control. Because if he slipped up, he could hurt someone, out himself, destroy his ability to be among people without quite being one of them.
And this too is out of love. He loves people, and he loves humanity. But in many ways he expresses this by keeping himself at a polite distance. Unlike Bruce, he doesn't paint himself as a loner, but for much of his existence he has few friends; he's isolated from both humanity and his own culture in ways more profound than almost anyone else can understand; he has a Fortress of Solitude in a place few others can reach, which is his closest link to his heritage on Earth. Superman separates himself from humanity, and this bleeds into Clark Kent as well.
I see nothing wrong with writing superbat in line with their friendship dynamic, with Clark being more open and Bruce more cautious. In fact, I think there's something interesting about their theoretical romantic relationship with each other being distinct from their usual relationship styles (e.g. Clark doesn't have to be cautious now because it's BRUCE, who already knows all his masks). But it would definitely be awesome to see more fics trying it the other way around once in a while. For instance, a Bruce who only holds back because he thinks his feelings are unrequited, while Clark knows it's requited but says nothing out of a fear of upsetting the balance. Superbat are so fun as a pairing because there's so much to explore there, so explore I say!!!