This will be a weird user experience in 1st person and may turn out to be quite annoying in 3rd person.
When you play as 1st person and wrestle camera controls from the player outside of a cutscene, you’ll lose the sense of being rooted in the character, which is the whole point of 1st person. May not work for everybody.
For 3rd person, the character would almost always be placed between the object and the camera. This means you need to push the camera through the player or move it close to the player’s body / head if it’s over the shoulder style cam. Or zigzag around the player’s mesh which is, arguably, quite strange.
This, of course, does not mean it’s not worth trying, and should not be too difficult to implement. Since it’s the player that chooses when to engage this inspect mode, it may not be that bad.
The objects have overlapping collision:
The script:
Feels quite sticky. With the mode engaged, if you move slowly, you will eventually end up strafing around the target 
Experiment, tweak it, you might be up to something. Who knows!