Why do we use fake handheld Motion
There are many cases why you would use fake handheld on your shots. For example, you have a VFX shot and want to add some life to it. Instead of having a static shot it now moves like someone was holding the camera. Giving it less of an artificial look. Next to this it can also hide small mistakes by drawing the attention away from them.
The second reason is for story telling. We all know camera movement can enhance the feeling in your shots. The less shaky it is it could mean the subject is in control of the situation or the environment is relaxed. A lot of shake can show that your subject is losing it, he is getting stressed. You can notice this a lot in war movies where they play a lot with going from a calm handheld to a heavy shake.