It is not wrong if we added 了 to the back of the sentence
Why is 去 (to go) not acceptable. 回 (hui) basically means 'to return' in this context. I would not say 'you should return home' in english.
In a previous example, 'she should not go to work', they used 去。 So what determines when to use 回 versus 去 ?
回家 is the usual way of saying "go home" in Chinese, because when you go home, you're usually returning home.
is “你应该回家了” wrong?