In all the apps I develop, I store tha last used directory in application settings (QSettings, i.e. the Slicer.ini file). It would be quite easy to add this to the DICOM import.
It could be that this directory shortcut available in the Import DICOM dialog box is handled by Qt itself.
On Linux, my Slicer startup script edits $HOME/.config/QtProject.conf to add a few directories to the shortcut key. Then the above mentioned dialog box shows the edited shortcuts.
But there’s a caveat. If just after starting Slicer, the Add data/Choose file(s) to add dialog box is raised, the shortcuts in that configuration file get overwritten to $HOME.
The workaround is good enough for me, your’s would be good enough for you. A general solution would be nice indeed, I have no idea if it’s Qt or application related.