I think there are many problems with the Local view.
@MaxPuliero explains one of them at the end of his video here.
I also created this post about the camera movement in local view.
Looks like there is no way to add objects to the local view, but you can remove objects. And removing objects will ask for a confirmation which is another annoyance for me.
Ideally I think it should work in edit mode too, for isolating faces, verts, etc.