Patton did receive substantial punishment, he was denied a combat command while his superiors decided what to do with him. In the end he was passed over for command of the First Army, despite being senior to Bradley and certainly more skilled.

Patton is a popular character now and a talented military leader but he was basically incapable of any kind of political work, which is necessary for a truly successful general. Patton was prone to outbursts and radical behavior. Many of his contemporaries, such as Bradley, and Terry Allen disliked Patton and found him difficult to work with.

The slapping incidents were conduct unbecoming of an officer. Although then known as "battle fatigue" PTSD was and still is a real wound with serious consequences and the fragile mental state of men who have endured combat was well understood. It was wrong for Patton to attack his own troops regardless about how he felt about the subject. Marshall and Eisenhower did not like that kind of behavior since it showed poor judgement and lack of self control. Self control was considered an important trait in Generals, for instance Terry Allen was a skilled General who led well in North Africa and Italy, but he was also relieved. Mostly because he was difficult and by all accounts a rip-roaring drunk. His staff often had to carry him around because he was stumbling with alcohol, so even with a good combat record it is still possible to be relieved.

Allen eventually earned another command, Patton suffered less mostly because he was necessary. Patton was an excellent general and possessed good leadership skills and instinct. Ultimately it was determined that he was to useful to the war effort. Eisenhower, though not particularly glowing of Patton calls him (I'm paraphrasing) "the finest general of pursuit I have ever known." Its somewhat of a backhanded compliment, since although he is calling him a fine general Eisenhower is pointing out that he is only really good at one thing, pursuing defeated enemies. It makes sense then that Patton really shines as commander of the Third Army which was... pursuing defeated Germans across Europe.

Really Patton should have been lucky he wasn't outright relived since that action was considered.