Have they ever been called out in the middle of the night?

They had the whole city blackout episode that took place overnight.

There was an episode not too long ago about a firefighter who used to sleep in his turnout pants because he was older and afraid it would take him too long in the middle of the night. They then got a call and it was revealed that Mouch does that too. So it was at least a call when they were all sleeping; not sure of the time of day.

It probably costs a lot more to do a night shoot and the showrunners/writers have gotten lazy.. Also, as a show continues, the cast end up getting raises which then decreases the budget for effects. Soap opera relationship drama is much cheaper to produce than exciting fires and rescues. Also sharing production resources with Chicago PD and Chicago Med cuts the window for shooting and post-production.