In 2.79 you could use a trick setting the view to Matcap and disabling the edges, to show only the vertices, in vertex mode, but in 2.80 it doesn’t seem to work like that.
Also, it’s strange that if you disable manually all the options in the Overlay pop down, most of the stuff stay enabled, while if you press the button, everything disappears, where are the other options buried?
In other software there’s an option or a script to do that, and most of the time, copying and pasting the output from a Blender command, gives you an error like that the attribute you are using, doesn’t exist.
You can create a different view with all overlay disabled, and work in the one you can see your vertices 
@uriel Viewing the mesh with wireframes off is also used in subdivision surface modeling to work previewing your edits without the wires to distract you. I made a post recently showing that (2.79).