How do I require users to populate the "Assigned to" field on artifacts?

You can do this on an update but not during creation. You do this using rules, and make the user attribute mandatory. Use the "action based dependency rule."

For example, when I manage artifact types on the https://mis.ibitdev.com/ project, the "Required" column displays "N/A" instead of a checkbox. In other words, why can't you make "User" attributes required fields in PT? Again, you can do this on an update but not during creation.