Current scenario:

The only option to have assignee required is upon changing the Allow unassigned issues setting under General Configuration, which affects all projects and forces the user to set Default Assignee for each project. 

Suggestion:

The user wants the Assignee field to be set as required and at the same time remove the Automatic assignee for a project, this allows the user to be able to assign the issue from a list of users instead of setting an automatic user during issue creation.

Work-around:

Unfortunately, this workaround is not valid for Atlassian Cloud. Assignee field can be marked as required upon using a 3rd party add-on, as per steps listed on this article.