Rich with does, I suggest, say something about the quality of something, and that quality is almost always positive.
He's rich with things that money cannot buy: friendships, supportive relatives, and a spouse who encourages him each step of the way.
The above sentence uses the word rich in a positive way, and doing so would seem to be the norm. I would not link the words rich with with negative things.
Maybe I betray a certain cultural bias in linking rich to only positive things, as if to be rich is necessarily a good thing. On the other hand, if irony is the reason for the link between rich with and the negative things, then the linkage would make sense, and to be rich is not necessarily a good thing. For example, if the "she," above, has great wealth, but her character leaves little to be desired, I might say ironically,
"Oh, she's rich all right. She's rich with a nasty disposition, a passel of enemies, and a cheapness that beggars description."
"Rich in" can be used, I suggest, in many of the same ways its counterpart "rich with" can be used, as in
The sub-Saharan country is rich in oil, manganese, and semi-precious stones,
Jim is rich in kindness, generosity, and thoughtfulness,
Sally is rich in friends, cheerleaders, and supporters.
In conclusion, "rich in" and "rich with" are virtually interchangeable. As for
The literature is rich with/in examples,
I suggest you be guided by whichever word sounds better to you, since they're both, as I said, virtually interchangeable.