Why can't I edit my birth surname?

Your birth surname was set when you joined, and it stays fixed because other relatives are connected to you through it.

A birth surname is one of the two facts that decide which family line a person belongs to. It is not a display preference: the trees of people related to you join yours through that name, so changing it would re-hang every one of those connections.

Your current surname is recorded separately, for the same reason in the other direction — it connects you to the family you married into. Keeping both means neither relationship is lost.