His injuries while fighting Windu were part of the plot to draw Anakin to the dark side. But was this detail planned from him? Did he plan to become burned? Or was this an unpleasant side effect he didn't foresee? Couldn't he manage to look defenseless and tortured by Windu to Anakin without sacrificing his health and his physical integrity? Perhaps a Sith with higher goals does not mind about this, but why take an even minor loss if not absolutely necessary? A crouched, defenseless, whining Palpatine, hardly holding back Windu killing him, would have had the same effect on Anakin I think.
Out-of-universe it's clear to me that they had to do something to explain the established look of him in the original trilogy.