The way I see it, the point of defining a point of sail has to do with the big picture....the boat relative to the true wind. Let's look at a Hobie tri-foiler or Windrider Rave...by Mike's definition, they are not capable of sailing downwind! They're apparent wind is always from ahead so they never beam reach or broad reach. What term do I use now to describe the direction the boat was sailing from A mark to C mark? "on the second upwind leg....".
OK, so that was a little silly but perhaps now you're thinking "well...no, Jake, you're talking about upwind and downwind and that's different". However, using terms like beam reaching and broad reaching simply define various points of sail between upwind and downwind. Just because you're carrying a "cooter valved magna flux spinnaker" and the wind is in your face doesn't change the fact that you are sailing downwind. By the same reasoning, just because the same thing happens at 90 degrees to the true wind doesn't change the fact that you are on a beam reach. If we only use these terms as it relates to apparent wind, these terms become exponentially less useful on faster boats until you're left with nothing but "upwind" to describe your point of sail. I offer the following diagram into evidence:
I would like to also offer another piece of evidence. Look at the Racing Rules of Sailing and you will find several rule references to "close hauled" ... such as (and I'm paraphrasing dramatically) a boat overtaking a boat from astern cannot force the boat past
close hauled . If this term is only used as an indication of where the sails are placed (as in beam and broad reaching), and I'm the boat being overtaken and headed up, could I simply pull my sails in tight, even though I'm at 90 degrees to the wind, and hail "sorry, I'm close hauled"?