As you say, your answer, at least in its recently edited form, does answer the question:
There is no shortcut that allows you to change the profile within the
terminal (without navigating the menus as you said in comments),
without the use of the GUI.
This does the work of Oli's suggestion that "No, there is no shortcut for this" may be an appropriate answer to the question.
So you're right, at least with respect to the current version of your answer. Your answer should be undeleted. The OP and other users can always downvote it if they think it's not good.
(That is not to say that deleting your answer was necessarily wrong at the time, since that was befor the subsequent edit.)
If I saw the current version of your deleted answer first (rather than this meta question first), I would probably have custom-flagged it to request undeletion. (Since we already have this meta question where it can be discussed, that's likely unnecessary, though.)