Good managers are able to allocate resources--particularly human resources--to complete a task. I know that it's a common trope to think that managers only take value instead of adding it, but it's simply not true; processes and production are less efficient without effective management.
People working in production shouldn't have to deal with clients/customers, nor should they be expected to coordinate with vendors, or even all other people involved in production. Production people are hired for their skill/expertise in production, so they should be left to do their job rather than taking on more jobs.
The flip side is that ineffective management can make processes and production less efficient than they would be without any management at all.