If you remove the Execute privilege for Assign action on Change, this also prevents the End user from progressing a change through an automatic assignment in the change process - (authorisation error).
You can do this by granting Execute, Read & Update privilege to the Role for Assignment under Change Management, Process Related Objects, Change. This will allow Create & Execute privilege. Then run the following SQL Server statement against your database (replacing Analyst with the correct Role Name), to disallow it as an action:
SET tps_value = 0
WHERE (tps_item_guid IN
WHERE md_name = 'ChangeManagement.Change.Function.Assign')) AND (tps_collection_guid IN
WHERE tps_name = 'Analyst')) -- Replace 'Analyst' with the correct Role name
Make sure that you have a full backup before running and test before applying live. Also, you may need to run IIS reset for changes to take effect.
ITBM 7.1 and above