Think OKRs.
"Is the high level goal for this software critical."
If yes. Then, people will give the problem the full attention it deserves.
And once you have their full attention, you are more likely to get their cooperation to being actually productive.
If no.
You're going to have a bad time.
I don't see how I should square that statement with your next:
Don't work on software nobody cares about
How do you know what software people care about unless you spend time working with the stakeholders?