While siankaan1's scenario is likely, I have certainly seen AA require customers to gate check bags when I know that there is space in overhead bins (either because someone has closed a bin that wasn't full, because a rollaboard was put in sideways, or through other inefficient packing). I wouldn't be surprised if the bins could fit 20% more bags than they do when "full". I think it's plausible that more efficient boarding could help.

(I probably did mentally conflate the statement that random boarding is fastest -- which I don't doubt in the slightest -- with the statement that it reduces gate-checked bags -- which I agree deserves more skepticism, though I do think it's plausible.)

I want to see the peer-reviewed study. There's got to be a Nature paper in there.