emacs-advice.el

  (defun org-read-add-default-time
      (&optional with-time to-time from-string prompt
                 default-time default-input inactive)
    "Filters the inputs to `org-read-date', setting the current time
as the default input if one was not already specified."
    (let ((new-default (or default-input (format-time-string "%H:%M"))))
      (list with-time to-time from-string prompt
            default-time new-default inactive)))
  
  (define-advice org-read-date (:filter-args (args) default-current-time)
    "Use the current time as the default input for `org-read-date'
unless one was provided."
    (apply 'org-read-add-default-time args))