This is the view in the root of the site:

This is the same view inside a folder; a new widget is shown:

This is a widget for folderish items so I agree it should be also present at root level.
There are other issues:
Edit come before Open in order to separate write operations from read_blank; it's misleading now. I don't think that in this case it'd be an a11n problem, do you @polyester?@davilima6 the first issue was already reported in #1126
This current-folder widget should not be present at Plone site root level. You don't want to cut/copy/paste a whole Plone site.
IMO, this widget has some other problems too: It duplicates some functionality already available in the button action bar above and you can achieve the same functionality, if you go a level up and select the folder to operate on.
Because of not optimal UX I removed it in this PR: https://github.com/plone/mockup/pull/651
Indeed, currently half of that widget's actions make no sense for a Plone Site object, as you said the copy/cut/paste ones.
Edit, Select all and Open do work however (the former curiously serving as an alias to @@site-controlpanel, maybe should be a more educative redirect) so I'm not sure if we should really remove the widget, thus making the _operate on current context story_ harder (having to go up one level). Or at the least less intuitive, leading to users to think "Why isn't it there/Why did it vanish? Oh, it's understandable but I didn't know the root folder was a different content type from normal folders. I'd expect just not to have nonsensical actions available there".
Most helpful comment
This current-folder widget should not be present at Plone site root level. You don't want to cut/copy/paste a whole Plone site.
IMO, this widget has some other problems too: It duplicates some functionality already available in the button action bar above and you can achieve the same functionality, if you go a level up and select the folder to operate on.
Because of not optimal UX I removed it in this PR: https://github.com/plone/mockup/pull/651