Core problem: I don't like the way how TcxGrid delete (that is initiated by the default Ctrl+Del shortcut key for the TcxGrid or by the Delete button of the cx-navigator) is working: it is simple and direct call to the delete of the underlying dataset, there is no TcxGrid(/DataController).OnDelete(Sender: TObject, var AHandled: Boolean)
event for the cxGrid or cxGridDataView. And from https://www.devexpress.com/Support/Center/Question/Details/Q308755/tcxgrid-deleting-record I understand that I can only configure the confirmation message, but I have no control over the Delete itself, i.e., I can not implement custom Delete and therefore I don't even try to ask for the straight solution of this problem. My question is about workaround.
That is why I am refusing to use cx-navigator and I opt to introduce TAction that handles Ctrl+Del shortcut key for the entire form. I have multiple grids on the form each with its own problematic Delete procedure that should be handled in non-standard way by the custom procedure.
That is why my DeleteAction determines the ActiveControl (TcxGridSite, TcxGrid) initially and then calls relevant Delete procedure afterwards. All that is fine. But some other components (e. g. TcxDBTextEdit) have default Ctrl+Del handling as well and that handling is very, very good. But if shortcut key Ctrl+Del is handled by action (and it is marked as handled even in the case when no active grid can not be found and therefor even in the case when ActionExecute has not done anything useful) then further propagation is stopped. That can be observed empirically and that can be seen theoretically from http://edn.embarcadero.com/article/38447 .
But maybe still there is some workaround how the shortcut key that has been processed by the ActionExecute can still be propagated further to the default components if they are Active controls.
I know that TAction is for (form-wide global) menu functionality but TcxGrid is not extensible enough and that is why should try to stretch the Delphi TAction design as well.