Because an exception for that was taken into account long before now, and trans people were not.
But just because the people that drafted this law didn’t write out an exception for deadnames doesn’t mean it’s inherently transphobic. This was hardly a major topic in the public discourse when these laws were made.
Again, a law that requires voters have transparency is a good thing overall. It needs updated, yes, but the problem here is how it’s being used as a tool to abuse. The law is to prevent fraud, but no fraud is being committed.