Leadership is not for everyone
Many people in organizations aspire to leadership positions. But it's not because they really want to lead people, and it's not because it's something they are really good at.
Many people who aspire to leadership are really seeking increased compensation and more respect from their peers. In traditional hierarchical organizations, this is the only way these people feel they can get those things. In old-fashioned organizations, this might be true.
But in modern, innovative organizations, this does not need to be the case. Create opportunities for your employees to get pay raises based on a combination of tenure + performance, not title. In meetings, you and your leadership team must set an example with respect to listening and valuing every person's input, and following great ideas regardless of where they originate. Find ways to acknowledge, and reward, employees at every level (even interns and brand new employees) so they feel respected and like equal contributors, regardless of their position on the org chart.
All who say they want to be in "management" don't actually want to lead, and might not be good at it. Help them get the recognition and/or compensation they deserve without putting them, and your company, in a position to fail.