This is a good example of how ADDITIONAL safety systems can sometime become the de-facto safety system. A similar problem can happen with firearms, where if a mechanical safety is on, people sometimes disregard other rules of safe firearm handling, leading to accidents.

Pilots have a lot of info coming in at any given time, and there has been a move to reduce the amount of info, so they can focus on the more important items. The answer isn't always more warning lights or alarms.

Edit: By "This is a good example..." I am referring to the hypothetical situation, I am not confirming this actually happened.