I think we're coming at the same conclusion effectively that introducing marginal pricing would be costly for the airline. I think the status quo, where coach overhead space is a race, is the best solution (to explicitly not solve it outside of business/first.)
That's not the issue. They have no marginal pricing, so the priced-in-ness does nothing to help ration that scarce space.
The issue is that passengers would viscerally hate it and a competitor would advertise "free" carry-ons and we'd be right back to the status quo.