Meanwhile it’s possible to hide the vertical tools pane in newer Acrobat Reader DC versions, e.g. 15.23.
In older versions, the user had to click the tools pane’s arrow button every time a PDF was opened.
Edit -> Preferences -> Documents -> Open tools pane for each document
(In German: Bearbeiten -> Voreinstellungen -> Dokumente -> Aktuellen Status des Werkzeugfensters speichern)
There might be some bad translation; the german one seems to be more correct. In fact, this setting saves the last state of the tools pane. So the user has to disable the tools pane once (e.g. via the arrow button), then it stays hidden for future PDFs.
If you want to deploy this setting for multiple computers (useful!), use this registry entry:
HKCU\Software\Adobe\Acrobat Reader\DC\AVGeneral\ -> DWORD bRHPSticky, Value 1