If you want unassigned issues in some places and not others, that's possible - in the project/issuetypes you want the assignee to be filled at all times, use the field configuration to make the assignee mandatory
JIRA doesn't support this in the "automatic" options (you can do unassigned, project lead or component lead), but if you always want to set it, you can use the "update field" post-function to set it. If you want it to be conditional (i.e. "if user leaves it blank, set it to reporter") then you'll need a spot of code to do the post-function
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