In a Scrum Team, we have 3 accountabilities: Product Owner, Developers, and Scrum Master. These are separate areas of accountability. So much that finding one person proficient in two areas seems like a big challenge (and risk). Practice suggests that Product Owner and Scrum Master are meant for 2 separate individuals. These are diverse environments, requirements, and skills. Too separate and involving to be effectively handled by just one person.
If you are still not convinced, imagine a paediatrician who is also a preschool educator and fulfils two roles in the clinic. It may be potentially tempting to imagine a doubly good approach to children and in-depth knowledge of their development or needs. But when the waiting room fills up with bored, crying patients whom the caregivers cannot control, which responsibility will prevail? To control all the patients or to examine the next patient in the queue? After all, both tasks equally belong to them.
Be aware that the Product Owner is not alone. They may delegate their tasks to other team members, but responsibility and decision-making always rest with the Product Owner.