The only responsibility for the IC would be stand ups with their manager to discuss progress and agree to future timelines. The ICs wouldn't have to go to any other Agile meetings or write any business/project planning docs. Manager would scope and write all IC tickets.
I think you would very quickly see a culture change with regard to process work. Having sole responsibility for both creating and completing the process work, it would be in the manager's best interests to make it efficient.
I've never seen an org try the above, but it doesn't seem crazy to me. I expect you'd still be able to attract managers through increased compensation and opportunities for career progression.
Note: I'm not saying the IC forfeits all planning discretion, I simply mean it would be the manager's responsibility to write it up into whatever documentation is required by the org, track progress, rewrite the plan as necessary, etc.