I should emphasize here that the checkbox also should not be shown by default, since it makes the stair stepping of the hierarchy more difficult to read:
To me, that is the wrong solution.
Users may want to hide things in viewport and see them at render.
An automatic override would simply remove that ability.
I prefer to simply enable Render restriction toggle in default startup.blend file.
Expert users may, and they still could. New users, however, wouldn’t have to Google why all of their hidden stuff suddenly show up in their renders, because the UI sure didn’t provide them with any clues for it.
No, you don’t have to be an expert to want to hide a ground or some walls of a room in viewport but have them occluding environment in render.
Why adding an artificial toggle there between Expert/Newbie when problem can simply be solved with a better default ?
Viewport and Render toggle are on same line. User can disable/enable both in one single movement.
This was my suggestion before UI Paper Cuts was closed.
Hide hierarchy in Outliner by default.
Example how it’s work in Modo
also hiding in viewport by H affect globally on hide object
(it hides from rendering too, in blender you need to search that object in outliner and manualy click camera icon if it turned on in Restriction Toggles),
and by clicking on eye in outliner it doesn’t appear until pressing Unhide (U in modo) in viewport
Similar as Blender Collection hiding in outliner but for all objects hierarchy