You can read the moral of Sandman as "Change Or Die", which is Gaiman's view, or you can read it as "Forgive". You can say that Morpheus died because he couldn't forgive anyone, least of all himself, and that lack of forgiveness eventually ate him away. There is only so long one can hate oneself before it becomes terribly self-destructive.
And the eating-away, the fighting with himself where he knew that he'd done wrong, couldn't admit it, couldn't forgive himself is what made it so that his enemies eventually managed to get around him.
Things started to really get bad after he'd had time to consider his past (while captured) and then had to face his biggest... call 'em "sins": Nada, and Orpheus. Now, the Nada issue was resolved well enough. He saved her, and gave her a new life. But Orpheus? HOW can you POSSIBLY recover from that?
Introspection is a virtue of thought; so its an indelible part of Dream. I'm reminded of a quote from a book:
"Their virtue was war, so the gods tested peace."
Morpheus got trapped in introspection, trapped in himself, and stopped paying attention to what was really going on. In a way, he became just like the most trapped of his people: incapable of separating what he thought from what was and seeing the differences.
So now we come to Daniel, who is just as introspective, but has less to be introspective about. As Dream he's been around forever, but he doesn't have many of his own memories, just generic Dream-memories. He's also got the virtue of forgiveness. He forgave Lyta for killing Dream, killing Morpheus.
The rest of that quote, however?
"Our virtue is peace, so the gods test war."
He's got to learn to at least reach out and see if someone will meet him half-way.