Inspector locking doesn't work with multiple selected objects

This is a real-world problem for me: I'm doing some GPGPU rendering and select all my temp render textures from code. Then I'd like to move stuff about in the scene to see what that does to my results. however, when I lock the inspector it only shows one render texture.

2) How can we reproduce it using the example you attached.
Create an empty project
Create 3 spheres
select all of them

Enter a new object name in inspector, observe that all objects are renamed.

Lock the inspector (using the small padlock top right) to keep showing the 3 spheres

Enter a new object name in inspector, observe that only one sphere in the scene is renamed.