As you see, there are some folks who leave the hens to brood in their home coops without having any problems. But I think it's ideal to give the broody her own private quarters whenever possible in order to avoid potential problems.
Chickens are not so much trend setters as they are fashion-followers. They like to lay their eggs where others have already done so, thinking "this must be a safe place to lay, look how many others have left their eggs already!" The sight of a brooding hen is exceptionally appealing. "Wow, she thinks that place is so safe she's decided to raise her family there!" The intruding hens can cause eggs to break in the nest, or push the developing ones aside so they don't get the warmth they need.
Broody Mama can also get misdirected on her way back from her daily coffee break, and go to set on another nest and leave her egglings to cool.
I also like to let the Mamas have their own place to raise their chicks. Some flocks will leave new chicks alone, others will peck them to death. Also, chicks will need starter feed to eat, which is more costly than layer feed, and lacks the calcium the laying hens need. Anyway, the Mamas will be ready to return to their flocks before the chicks are fully grown, so it helps to have a separate place to keep the chicks.
Keep in mind that when you hatch out chicks you'll probably end up with more roosters than you may want to keep, be sure to have a good Plan B for them. If that plan involves getting rid of them in some way, make sure your kids don't get overly attached to them. Have them practice saying "IF this is a hen that we're going to keep, we'll name her..."