Dan Green wrote a thoughtful essay about literary coincidences. Click more to read my reply.
First, it’s interesting that the picaresque has pretty much disappeared in the contemporary novel, which tends towards the formal, the baroque, the introspective.
The decline of the picaresque form may have something to do with the emphasis on character autonomy and the deemphasis on external forces (fate, the gods) from determining outcome.
On the other hand, perhaps when we say picareque, we are merely referring to more open-ended forms with episodic content. In that case, then we can point to TV shows and sitcoms as continuing the picaresque tradition.
I would group the picaresque/coincidence connection with the problem of the limits of fantasy. How much can a dreamer/fabulist get away with? And if literary coincidences have value in helping the reader/viewer to imagine the improbable or laugh at fate’s silliness (see Candide), then they may very well reveal our own sense of helplessness combined with a desire to have our lives arranged as whimsically as certain literary characters. It may also reflect a discomfort with introspection. In this modern age of anomie, the individual reader may be uncomfortable with exploring characterization and emotions simply because solitude is dull and overdone. (I say this as someone who works in complete silence in a cubicle all day; when I come home, I am content with the shallowness of Cheers. It provides company and gets me out of myself).
Kundera has written about the picaresque character at several places (especially in his essay on Diderot’s Jacques the Fatalist. Kundera talks about characterizations arising from actions or situations (something Kundera links to erotic adventurism) rather than from internal drives. This parallels (for me at least) people’s affection for sitcom characters. The characters of the Friends TV show, for example, never have emotional depth, but the accumulation of backstory creates complex storylines in the 10th year. You can’t help it.
One final thought. I am struck by how the recent renaissance of oral storytelling has resulted in looser narratives and an emphasis on natural flow of speech rather than the contemplation of a phrase. Later generations may look at 19th century craftsmen like Flaubert with awe combined with incomprehension.