Indeed, “Comment se fait-il” does not mean the same as “pourquoi”, as both of them require an explanation.

On one hand, use “Comment se fait-il” when you require an explanation about something that happened, when you expected the opposite. This idiom precise some kind of surprise, disappointment or anger.

On the other hand, “pourquoi” is more general and does not carry those undertones.

Finally, “sitôt” is not much more formal, but this word makes the sentence shorter. Indeed, if you want to use “dès” conjunction, it requires a subordinate clause :

Et comment se fait-il qu’elle ne m’ait pas amnistiée dès qu’elle fut couronnée?