I used to get old executioner's plenty on Draven after boots and a doran's. It gave no AD, but Draven can handle that because he can last hit just fine anyway with his Q. In exchange for the lower initial AD compared to other routes, I got crit and tons of life steal fast, as well as an active I could spam in fights or totally mess with the support's healing by doing it right when their heal CD is up, and a passive that syncs perfectly with the play style of Q poking once then backing off to catch it. Draven loves both crit for his passive and life steal because he overkills the minion lasthits with his Q, which the life steal applies to.
In addition to giving me an even more godly lane phase, I could get infinity edge straight after while retaining the ability to heal up like a bloodthirster rush would have done. The stats synergize with infinity edge perfectly.
But now we have this item, which costs closer to 2/3 of a bloodthirster than 1/3 of a bloodthirster like old one, lost the massive life steal in exchange for a stat you'll build on your next item anyway, and lost the damage over time effect. The heal debuff applies on autoattacks now for 1.5 seconds. Just like I could apply it at almost exactly the same range for 8 seconds by pressing '3'. So much work moving my index finger up a centimeter.
I... can't see why I would ever build this. It still doesn't fit in my endgame build but now costs more and thus is more of a gold sink when I sell it late game. Its base stats are the same as infinity edge but far less - if I would ever want to build this item for stats, I would go for infinity edge instead. So that leaves the active. Which is a much weaker version of the old one that you at least don't have to move your index finger for. Maybe I would still want to use it anyway? I can't shut down the enemy support's lane healing with it, really, because the effect doesn't linger unless I keep attacking. It still works when committing to a to-the-death fight where it might mess up a clutch heal and we didn't pick up ignite for some reason (ignite being used only in to-the-death fights). That is literally the only case I can possibly think of where it would be better than the standard build, and that's only if the standard build didn't do enough damage leading up to and during the fight to counter half a heal.