This is the answer. You can solve this problem with tools; you don't have to change your philosophy. When your company has 5 projects, do you count Project Z's

This is the answer. You can solve this problem with tools; you don't have to change your philosophy. When your company has 5 projects, do you count Project Z's backlog against Project X's backlog? No you don't, even though they are both in the same database. The reason you're OK with this is because your teams' views have been adjusted so that they only see their own project. So they each see what they consider to be their own backlog. Use the same approach for low-priority requests: put them in the same database, but don't elevate them to the team's backlog view. If someone has an idea or a request you should not suppress it entirely. That will only encourage people to add yet another system of logging to your organization. Just because a request is not urgent or can't be put on the roadmap yet does not mean it's not important. And why throw away what can be logged for later archeology? "Oh hey the answer to this new problem is right here in this old request we never got around to."