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In KDE4 was introduced move window by clicking left mouse button on empty window space. Now, some window of plasma5/systemsettings5 was moved to new framework for write desktop/mobile apps, so this behavior is broken. I propose one of following:
1. Click on empty space, hold and move mouse to scroll - double click, hold and move mouse to move window
2. Allow to set device-dependent shortcut, so my touch-aware screen will scroll window content on click on empty space, but my mouse will move window on the same action

That drag-from-window-background feature is provided by the Application Style and may be configurable via the style's configuration.
In Breeze, that is configurable via System Settings > Application Style > WIdget Style > (with Breeze selected) Configure... > General > Windows' drag mode.
For Kvantum, that is configurable via Kvantum Manager > Configure Active Theme > Miscellaneous > Drag From.

As for customizing it to provide click-and-drag to scroll, I think that could be useful in certain scrollable views, though you'd need to be careful that it doesn't clash with click-and-drag to select, drag-and-drop or other such functionality.

As far as I know,, this is not only style-related.
Widget must tell X/WM it provided this behavior.
Maybe I'm incorrect.

But Discover use "drag-to-scroll" on empty spaces instead of "drag-to-move". I thought this inconsistency was made by Kaligrami(?) .

You are mostly right, the kirigami widgets are taking over the empty space so the application style doesn't detect that you click-and-dragged in empty space in order to trigger the drag-to-move behavior. Of course you also ran into that with other applications if they covered the full application window with other widgets.

Sorry for write in this topis far time ago, but I have an idea.

What about this? Application could bind actions to widget. Widget will have signal "select action" or similar. When default callback is set to this signal, widget will display menu of all possible actions, when user hold left mouse button on it. What about possible, default actions for all widgets:
1. Click
2. Move window
3. Zoom out, so user could select visible area of widget
4. Click for specified time
5. etc.