To answer your question : An assignment urgency can be independent of work urgency right?
Yes it can be in some cases. But in most of the cases assignment urgency should be reflected from work urgency as well. E.x. If Claim case have an SLA defined with Goal as 10 days and if assignments are not yet completed. After 10 days work urgency will change on case SLA and make it high priority case. Same urgency needs to be drilled down to all the assignments as well since assignments are the actual work units that completes the case.