One of the complaints about fiction is that so many times a plot is predicated on a number of coincidences. If things X, Y, and Z don’t all happen to the same person, then there would be no story, and what are the chances of that? I’ve always found this a little unfair.
Every day of every person’s life, there is a story to be told. Most of them are boring. They do expected things, with expected outcomes, and no one would want to read about that. A well-developed fictional world would be much the same. You don’t care about the butcher’s day cutting meat or the student cheating on a test, getting caught, sent to detention, and serving that detention without incident. The story of the conformist, the obedient, the rebel that gets squashed … those aren’t good stories.
So what makes a good story? The unusual. The noteworthy. The coincidence. Yes, coincidences make fiction interesting. It’s not hackneyed storytelling, it’s selection bias. You aren’t reading stories in real time, as they take place. You’re being told these stories after the fact, presumably by someone who has chosen them because they are interesting, unusual, and because they were the stories where lightning struck twice, the stars lined up, and a series of unlikely events coincided to make for one great story to tell.
As writers of fiction of course, we put the cart before that horse and make it push. We make up stories that include all the coincidences because it wastes everyone’s time to tell the boring stories that should make up the lion’s share of what goes on in any world. The fact that we never had those stories to tell doesn’t make a fictional world any less real; it just means that you need to imply that those mundane lives exist out there.
Now it’s certainly possible to go overboard. It’s a pitfall of long-running series that it starts becoming just a bit too much of a stretch. You can lose that suspension of disbelief that let you get into the story. “Really? They terrorists attacked on Christmas again and he’s the only cop around to stop them?”
Don’t be afraid of writing coincidences, and don’t be afraid of the critics who pan them. People will complain about anything. Just be judicious, and try to make sure you pay attention to keeping the individual stretches of credulity under control.