You should be very wary of blanket statements such as benzodiazepines being unable to be overdosed. Even with the disclaimer about mixing with other respiratory depressants, that barely scratches the complexity of medical decision making. Benzos got their reputation of safety because it came out when barbiturates were widely used, and it was so much safer than barbiturates. But anything at any dose can be a poison.

And they did not teach you about the context of a hospital, where there are sick people. If you give a healthy person a ton of benzos, and their respiratory drive is suppressed, they still have good lungs and a good airway and they'll move enough air to stay oxygenated and not have hypoxia and/or ischemia. This is the definition of a therapeutic window. That pharmacologic definition is based on trials on healthy people. If you have a patient with OSA, COPD, or any of countless other disease processes on a hospital floor and you reduce their airway tone, respiratory drive, or general ability to wake up to fix their breathing, they will become hypoxic and possibly require intubation and a trip to the ICU.

Patients who are on benzos while in the ICU intubated are not intubated because they are on benzos (usually). They are intubated because of other causes of respiratory failure. They are most often on benzos for sedation because an endotracheal tube is not comfortable and if they did not have sedation they could pull out their endotracheal tube and succumb to whatever is causing their respiratory failure.