About the RuneTerra map...

why would death have a birth place

Some champs are not connected to the map by Birthplace, they are connected by "place where a story about them occurs"... Considering that, they could be linked to Ionia since "A good death" happens there as far as i know.

Death is everywhere. Their existence started with very existence it self.

They have lore connecting them to a location. We just don't know where it is... probably the Blessed Isles.

They should probably just be put into every list for list of champions that live there.