Successfully providing feedback this way requires you to trust the people you've empowered to have the final say. At the same time, it requires the team to maintain an open-mind and, if need be, defer to your better judgement. On both ends, it requires the subjugation of egos for the sake of doing what's best for the company.
If that sounds like a difficult balance to strike, that's because it is.
A tough balance, for sure.