I think you hit the nail on the head.
My personal thought is that trainees should stimulate the muscles in various ways to make them stronger overall. As a result, varied stance/grip/body position in a limited seting would be great. However, on work sets, I believe the stance/grip/body position for the clean and snatch should be the same - or as close to the same as possible.
Deadlifts would be seen, in my opinion, as an "assistance exercise."
I too see the regular deadlift as you've described - hip is lower. torso more upright. distance of shoulders in front of the bar is less, more vertical.
For me, I get more engagement from my quads with the "clean deadlift" as you've described it. When I raise my hips more to get my shoulders in front of the bar to get in the position to perform a squat clean - I really feel a pre-stretch on my hamstrings and the hamstrings simply raise my hips and shoulders at the same time during the first pull.
On both the clean and the deadlift - I push my feet through the floor and bring my hips to the bar - but for me, the clean actually engages my lumbars more. It could just be me. But that's what I observe.
Don't know if that helps any?
All the best,