However, this seems against the spirit of the gameplay, and no similar action can be done with the Mage, and the rules are not clear.
The rules are perfectly clear. It is not only allowed, but actually a deliberate part of the game.
And natually the rules of the two actions are not similar: they are two different pawns; they are not supposed to work the same.
So, in MY turn I will certainly move the witch, if it is in my way. Unless I can't score anything myself and YOU will lose lots of points if when your witch-infested city is scored!