Cases Created From Salesforce Experience Sites do not Trigger Case Assignment Rules

As a workaround, you may want to consider creating workflows or triggers to route the case to the appropriate queue or user if the case origin is the site.

Vote and comment on the following idea to change the current product behavior: Case assignment rules don't fire on the new community.

Note: The Case Assignment checkbox was available before the Winter '19 release in sites that use the Salesforce Tabs + Visualforce template. The checkbox was removed after the Winter '19 release, as this was determined to not work as intended.