Medic, that's pretty much my opinion that I stated earlier. I handled a 580 once. The assist was much nicer than the 670 I had for a week during a Passaround. It has a more positive feeling than pretty much any torsion-bar based assist, like the 670 or any of the Kershaws, since it's sprung for the whole arc, whereas the torsion-bar assisteds ride on inertia for about half the arc.
But again, as nice as the action feels on the AXIS-Assist knives, it seems so pointless. I never liked assisted knives that used thumbstuds rather than a flipper, as it's easy to slice your thumb open if you're not used to the action. And besides, as you, I, and thousands of others have found, the AXIS lock is so extremely easy to flick open with your thumb already; it's like trying to make your gun more powerful by running behind it to give it extra speed. I guess it would be useful if you're old and/or arthritic or have a similar impediment to hand strength or dexterity, but for most of us, it's pointless.
And of course it completely kills the ability to wrist-flick the knife closed, just like the Auto AXIS. That's what I like so much about my 940's. Flick it open, flick it closed. Only need one hand, and you never have to put fingers in the way of the blade, or close it against your leg or something. Along with a D/A OTF auto like an Ultratech or Scarab, it's the safest folding knife you can have.
I'm guessing that Benchmade is using the AXIS-Assist because assisted knives are "in". For years the AXIS lock has been their flagship locking mechanism. Strong, ambidextrous, easy to use, etc. And now that they've figured out how to make it assisted (not just automatic, making it legal in many more places), that's their new gimmick.
I'd like to see the 581 in a non-assisted version, but to be honest, I don't know that I'd buy one even then, regardless of how super the steel is. For me, the 940 is just about perfect, so any new knife will be measured against the 940 and will likely be found wanting in some way or another.