✨Accruing all credit to a team manager for their team's achievements, and paying them more because of it, is some disempowering bullshit holdover from the factory day.✨
Taking credit for another person's creative output is stupid, and rightly galling.
If management isn't a promotion, prove it: pay the same (or less!) than engineers of the same level. The people who still want to become managers are the people you actually want managing.
Not the problem. Plenty of them are curious about managing, guaranteed. The problem is your incentives are set up so that only sociopaths will ever want the gig.