I seem to remember AA agreeing to valet check a bag (instead of gate check) when in domestic first and there is no bin space left.

Has not happened to me though in years, ever since the new bins are widespread. I am often one of the last to board, and when in F the gate agent has always let my bag on. And there has always been space to find onboard with the new bins. I think this is a major perk for F, essentially being guaranteed bin space even if last to board.