The Product Owner wants the Developers to adhere to its Definition of Done to have complete transparency into what has been done at the end of each Sprint. This is because:
The Definition of Done is a formal description of the state of the Increment when it meets the quality measures required for the product. It is a shared understanding among the Scrum Team and the stakeholders of what “Done” means for any Product Backlog item that is selected for a Sprint.
The Developers are accountable for creating a “Done” Increment in every Sprint. They must ensure that every Product Backlog item they work on meets the Definition of Done before it is considered complete.
The Product Owner is accountable for maximizing the value of the product resulting from the work of the Scrum Team. They must inspect the Increment at the end of each Sprint and assess how it delivers value and contributes to the Product Goal.
Having a clear and consistent Definition of Done helps the Product Owner have complete transparency into what has been done at the end of each Sprint. It also helps them make informed decisions about releasing, adapting, or continuing the product development.
Other options, such as predicting the team’s productivity over time, knowing what the team will deliver over the next three Sprints, or reprimanding the team when they do not meet their velocity goal for the Sprint, are not valid reasons for wanting the Developers to adhere to its Definition of Done. They may reflect a misunderstanding of what a Definition of Done is or how Scrum works.
References:
[Scrum Guide], page 10, section “Definition of Done”
[Scrum Guide], page 7, section “Developers”
[Scrum Guide], page 6, section “Product Owner”