The point is that there is more risk of a serious issue with a generator than without. The degree of risk varies with the type of equipment, the type of installation, the conditions present at the time of usage ( windy, calm ), the effectiveness of the maintenance program.
It is vitally important to recognize that there are risks. It is equally important to minimize them. You can minimize the risk with the use of CO detectors, fire detectors, an alert human watch, or simply avoid the risk in its entirety.
The decision rests on the shoulders of the Captain. There are desirable benefits with continuous usage of the generator. It is up to the Captain to determine of those benefits are justification for accepting the risks. Note that, other than not having a generator, you cannot remove the risk, only reduce it/manage it.
It is a command decision, and the variables that affect that decision will be different every time the decision is made.
Whichever you choose, please do everything in your power to keep all risks at an absolute minimum. Be safe. Be happy.