What is the purpose of the default owner in the category values set up
I know what I would like it to be
That I can set the ticket owner based on the category but I cant seem to change the value from Unassigned.
it works as you assume.
You need to have a label with users who can own tickets in this queue. Then you can click to edit to choose the user you need.
Or to translate Nico's answer, to be able to edit the category and to assign a default owner for that category, the owner you want, must first also be a member of the user label that you are using under "Owner Labels" on your Queue Configuration page. You can then click "Customize fields and layout" and then click the pencil Icon to edit the category and select your user from the names in the dropdown ;o)