But I'm assuming this means hiring people without the same transactional mindset? Otherwise, there will just be endless employee churn as they realize there's nothing in it for them.
It's hard for me to get on-board with a management approach that effectively says, "I don't want to do this stuff because I want to get paid but it's okay for you to do it because I don't care whether you get paid or not." Either you think the work is worth doing or you don't, but it's a weak leadership style to say it's only worth doing if someone else is doing it. (That's different that strategically assigning duties to get the most out of the team.)
Unless you want to get promoted into management...
Hire new people to do the inglourious work.