I do believe the reason you provided it accurate. I do believe people that are using it for that reason likely didn't really think it through.
It is kind of like the Six Million Dollar man running in slow motion with sound effects was used to convey running really fast. That didn't get used too often outside of that series.
The most immersive action movies of all time did not use shaky cam as far as I know. Kind of like when you run you are not viewing your world as bobbing and weaving. Kind of like how if you normally get motion sickness riding in cars you might not if you drive because the car becomes a tool and extension of the driver's body and they do not really notice movements that occur in ways alien to their mind. The shaky cam is like the motion that causes car sickness. It is the image moving one way when your mind thinks it should be going another.
A good film should not really want people focusing on that.