Most canyons on the Colorado Plateau do not have good cell service and are rarely visited. This means that if you or someone in your group gets stuck or serious injured, the only way to get help is for someone in your group to finish the canyon, get in the car and drive until you can get cell signal. Then Search and Rescue (SAR) will have to mobilize, often dispatching a helicopter from up to a hundred miles away. SAR takes the safety of their team members very seriously, so if it's not safe to perform a rescue in the dark, they will wait until light the next day. So more often that not, if you get injured in a canyon, there is almost no chance of rescue the same day. At a minimum, you're looking at spending the night in the canyon, injured, and very very cold.
When canyoneering, you need to have a contingency plan for how to survive if somone gets stuck or injured. You need to have access to extra food, water, first aid, clothing, and possibly overnight gear. This could be on your person or at your car if your car is close enough for any one member of your group to make the trek alone.
Injury is not the only way to get trapped in a canyon. Exhaustion and a slow pace have cause many groups to have to spend an unplanned night in a canyon. Additionally, sticking or damaging a rope, or losing some key piece of gear could also strand your group. You should always have enough gear to finish the canyon, even if something gets lost or damaged. The general rule of thumb is to have at least as much rope and 3x the longest rappel.
You should always have someone not on your trip that knows your itinerary, which canyons you will do and what time you expect to be finished. It sucks to have to be rescued, but it's even worse to need rescue and not get it.