Do We Really Need a Full-time Product Owner or Scrum Master
Most managers, when they see the designation of specific roles such as Scrum Master and Product Owner worry that if they identify people to take on these roles then they immediately are reducing the capacity of the Team and so the Team will produce less work.
The result is that management will try and skimp on these roles. This is a mistake. When adopting Agile there is a reason we establish these roles: our aim is to create a Team that can produce more than the sum of its parts - a high performing Team.
These specific roles help establish a such a Team with the Product Owner focusing on controlling the intake of work to maximize return, and the Scrum Master focussing on Team improvement. We are in fact establishing a new system, a new way of operating. If you skimp on these roles, you can be sure that capacity to deliver of the Team will be reduced as you try to do too much with your people. Further, improvement in Team performance will be much slower.
At a minimum you should try the new roles, the way they were intended, before making adjustments. Perhaps your situation really is different and will need different innovations. Before you can make that assessment you need to determine pros and cons of the recommended approach and use that information to improve your implementation.