Incentives operate on a slow time-scale. Let's say you have a decent team as a baseline, but starting to fall into this "just tell me what to build" apathetic failure mode. How would you turn this ship around?

As a manger, you could go as far as saying explicitly -- "hey, any engineer who demonstrates customer obsession and shows attention to impact, will receive their choice of project to work on, will get promoted faster and higher than those who don't, etc.", but this is unlikely to create a positive outcome. At best, 1-2 people may rise up, but the rest of the team will resent them for "try-harding" probably; crabs-in-a-bucket mentality is a very natural human group phenomenon. And now you've got 1-2 "stars" who won't want to stick around to deal with the rest of the shitty team members, so once they leave, you're back at square one.

Reorging is a reasonable step to take, but it's risky and you could just as well end up "infecting" other orgs or team members, by carrying the contagion of bad culture with you.

Firing and hiring again more carefully, is honestly both faster and more direct, and shouldn't be seen as a "last resort" option IF the culture is truly too far gone AND the culprits are readily identifiable. First step is probably to make sure you have a firm and accurate diagnosis of the problem, then if you're 99% sure you can identify the right people to fire -- go ahead and fire them.