As a statusless, almost-all-the-time-Y-class flyer who is not pinching every penny, I love this idea. If it were up to me, I would allow people to reserve and pay for the overhead bin of their choice.
The current system is backwards. It encourages battling for space by rewarding the "winners" both monetarily (no checked bag charge) and from the baggage carousel/risk of loss perspectives.
Make the checked bags free and charge for reserved overhead bin space.