If you want teams to care, they need to own it. When teams care, things happen faster. The catch is that you can't make them care about what you want done. You need to treat the team like the "10x rogue developer" giving them freedom to pursue what they want to pursue, steered by the product owner, shielded from external stakeholders. A product owner that mandates as _part_ of a team "we need to do X by y because Bob from marketing wants it" has a losing battle on their hands.
I really think the best person to be prioritising is the leader of the moment. Sometimes it's the strongest Dev, sometimes it'll be the product owner, sometimes it'll be the scrum master, sometimes it'll be a UX designer. It could be anyone, that everyone believes in. The next week/month/quarter it'll naturally be someone different, or maybe it's still that same person, if everyone is on board then there's no issue, right? That's not to say there's should be bitter infighting either, only that everyone should follow the herd. This way, the majority of people believe they're working on the right thing, and social pressures get others pushing in the same direction too.