I recall the x-com series allowing you to pickup fallen, still living comrades, although I think that was a pretty questionable tactic considering you were better off killing everyone in the vincinity and then attempting to heal the fallen.
Silent Storm (and SS engine utilizing games) also allowed you to have characters pickup fallen characters and carry them on their back. Although again, the use was pretty questionable considering it took a LOT to kill one of your soldiers (they wouldn't die unless damaged further when on the ground) and enemies would never aim at those already fallen. It was really only useful when kidnapping some enemy officer as a mission objective.
Also, there was this one obscure, supposedly not very good, game called Combat Medic. Although whether or not it featured dragging, I don't know as I've never played it, but there is the possibility. All I know is you were supposed to heal wounded comrades on the battlefield.
the problem is,
Many gamers nowadays care more for shiny graphics and PewPewPew moreso than Cool new features.
if anyone on the forum is interested, i'm pretty sure we could MAKE a game such as this, source engine would be preferable.
i know it'd be a big undertaking, but it's your best bet if you want those sort of features.
( i can do maps)
A game about dragging wounded comrades? Well, that's pretty much WWI Medic, really.