I understand your view. From the user perspective inline task are still more a specialization of a task, which is a specialisation of a heading.
Here is my implementation of how I see it that it should behave:
(defun pm-cut-special ()
"Like org-cut-special but also works on inlinetask."
(interactive)
(if (not (eq 'inlinetask (save-excursion (org-back-to-heading t) (org-element-type (org-element-context)))))
(funcall-interactively 'org-cut-special)
(org-inlinetask-goto-beginning)
(let ((begin (point)))
(org-inlinetask-goto-end)
(kill-region begin (point))
(message "Cut: Inline Task"))))
(defun pm-copy-special ()
"Like org-copy-special but also works on inlinetask."
(interactive)
(if (not (eq 'inlinetask (save-excursion (org-back-to-heading t) (org-element-type (org-element-context)))))
(funcall-interactively 'org-cut-special)
(org-inlinetask-goto-beginning)
(let ((begin (point)))
(org-inlinetask-goto-end)
(copy-region-as-kill begin (point))
(message "Copied: Inline Task"))))
(defun pm-paste-special (arg)
"Like org-paste-special but also works on inlinetask."
(interactive "P")
(if (not (eq 'inlinetask
(with-temp-buffer
(org-mode)
(insert (current-kill 0 t))
(goto-char (point-min))
(org-element-type (org-element-context)))))
(funcall-interactively 'org-paste-special arg)
(unless (eq (point) (pos-bol))
(forward-line))
(yank)))
There is a fine-tuning outstanding: The criteria whether to paste before or after the current line should not be the point on the begin-of-line but the beginning of the actual heading (after the asterisks).