There is a different way of picking up a downed teammate or AI that i think looks really cool. I believe its called the ranger roll wit a fireman's carry but don't quote me on the name. Heres the link. https://youtu.be/KPrATJ-u5Rg
This has been discussed on these forums before. It would be great to be able to pick up dead bodies this way, but if you did this to an injured team mate, you would most likely do more harm than good.