This is a major problem.

E5, E6 thinking they are leads and managers = can push job

M2, M3 doing technical work thinking they are seniors why should they accept the job = reject

End up the poor E5 with just engineer title will take all the workload.

The biggest disparity I knew was the PM was E6, a team lead was M3 but the E6 manage to push all the work to the M3 simply because the bosses like the E6.