If the form is successful, sure you can go to another page. When submitting the form however, you typically submit it to itself in the case of the opposite outcome, it is not successful in which case you would show the error message. Now having said that, it also depends. In many cases the form may show a successful and still redirect back to the form. Think of a form that “saves”. Sometimes you redirect back with a success message only to show the form again for future edits.
Now if you were referring simply that they could just redirect if the outcome was successful, then I agree. I was just saying that in most cases you submit to itself and if it is successful, then do something. Otherwise you want to go back to the form again with an error message so the user can try again. If I misunderstood your statement, then I apologize. But I do stand by the idea that you typically would submit back to itself because a success doesn’t always mean a separate page. I was also under the impression you were also saying a separate page for failure as well.
But in any case, the typical pattern is you submit the form back to its page, if successful do something and if not, show the message and display the form again.