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Currently, Microsoft does not allow DELEGATED ADMINS to manage Job Queue or Data Migrations and a separate user account with a separate license has to be configured to provide this work to a client. PLEASE update the system that a DELEGATED ADMIN can manage Job Queues and handle data migrations.
STATUS DETAILS
Declined
Ideas Administrator

Thank you for your feedback. We are not considering the suggestion at this time due to the following reason: 

Both processes allow a process to be run in the background and at a later time from when the Delegated Admin sets it up. It is possible then, at the time of the job queue to run, the Delegated Admin user has been removed of such role and process runs without the appropriate license. 
Job Queues can be run once in foreground for test purposes (available in 2021 Wave 1) and therefore the Delegated Admin is able to test the job queue. Still, in order to set up a job queue to run in the background a full license is required.
 

Sincerely,
Tomás Navarro
PM, Microsoft