Google tried this in 2000, it was an absolute disaster.
Managers also:
1. Handle administrative concerns like requests for leave, vacations, illnesses, deaths in the family, etc.
2. Understand each of their reports' career goals and try to put them on projects where they can grow & contribute best.
3. Handle personality conflicts between individuals on the team.
4. Make sure that individual contributors get recognition for their work.
5. Encourage their team to keep going in the face of obstacles.
6. Protect their team from interruptions by handling many of the external inquiries themselves.
7. Connect team members with relevant collaborators in other parts of the organization.
Now, there are good managers and bad managers, and typically good managers will do more of the activities on my list while bad managers will do more of the activities on your list. But that isn't a reason to get rid of managers entirely. Rather, it's a reason to invest in manager training, make sure they understand their role, and ensure that you've hired good managers and fire the bad ones.