The new design is just terrible for people who wanted DH for its stacking fantasy scenario (with the weaker early game that entails). This is just a brainless rune now. You don't have to consider how you'll path to maximize stacks in jungle, about how to position in teamfights to pick up that critical soul and snowball through the fight etc. It becomes just another "more damage for your damage" rune with no real thinking about how to optimize it. You just go in to burst as usual and then hope to proc. it.
The old DH had actual strategy behind optimizing the stacking and positioning in fights to utilize it (even small things like backing next to a cannon that will die under turret etc.). It's a rewarding design and gives junglers something for more pathing and late game oriented play styles. It's one of the few times that junglers can actually play for more late game power without totally sabotaging the team with picks like Amumu or Yi.
The new one is just basically always better on laners for stacking and is NOT AT ALL THE SAME IDENTITY! It doesn't even deserve the same name because it sure as hell isn't the same rune. You can make a new one if you want but don't ruin DH and turn it into this lame and less versatile version. The new one is also far more niche. I don't know why it's even being considered. I can see Kha liking this but not everyone who wants DH has strong up front burst to get someone below 50% HP and there isn't even an alternative stacking mechanism outside of that.
I don't think picking up the souls should change in any way. It's the best part of this rune and a mini-game that involves thinking on multiple fronts. Don't turn a good design into something so uninspired. I still miss the Smite buffs and this will be yet another blow.