As a freelancer I saw many companies, many situations and worked with many Project Managers, Product Owners, Scrum Masters and god knows what names the HR department came up with.
What is most important, in my experience, is that the people leading the team try to focus the people in the group on as few common goals as possible during one sprint. The more stories or goals the team has to finish, the more individualism and the fewer things will get done (with done being defined by your definition of done).
Differently put you should try to make your team work like how a soccer team plays. You try to make three, four or five goals per sprint. But you do this as a team.
Example: When a story isn’t finished at the end of the sprint; it’s the team’s fault. Not the fault of the one guy that worked on it. The team has to find a solution. If it’s always the same guy being lazy, that’s not the project’s or the team’s results. You or HR deals with that guy later. Doing so is outside of Scrum’s scope. It’s not for your retrospective discussion. But do sanction the team for not delivering.
Another example is not to put too much stories on the task board and yet to keep stories as small and/or well defined as possible. Too much stories or too large stories will result in every individual picking a different story (or subtask of the larger story) to be responsible for. At the end of the sprint none of these will be really finished. And the developers in the team won’t care about the other features being developed during the sprint. So they will dislike having to review other people’s features. They’ll have difficulty finding a reviewer. They won’t communicate with each other. They’ll become careless and dispassionate.
Your planning caused that. That makes you a bad team player. The coach is part of the team.