As much as I love "The Naked Time", this is the ultimate facepalm moment. There's also the time travel that makes zero sense. Then, you have an Engineering deck with only one entrance, and a Chief Engineer and his assistant both leave the area while in a tight and dangerous orbit because "they are wanted on the bridge", when they simply could have called up.
Lots of Star Trek over the years have plot holes and stupidities that should break the space-time continuum.
Agreed. We're suspending disbelief in order to be entertained - all of the ST universe has counted on the ST fans ability to suspend disbelief to one extent or another.