I know the "knee drop" as bleeding control is something that used to be taught back during the early years of the invasion of Iraq and Afghanistan, but my understanding is that it caused far more issues than it really solved. The application of direct pressure doesn't really care about what you're applying the pressure with, but the problems stem from the fact that you don't get as much high quality feedback from the knee as you do the hands; which, assuming we're talking about a gsw to an extremity, can lead to turning a fracture into a complete break as a result of putting your entire body weight onto the patient increasing blood loss instead of minimizing it. Coupled with the fact that it was intended to be used while under fire where stress leads people to over applying pressure you end up with severe complications that could have easily been avoided.

Also, on principle you should be able to open and use all necessary materials one-handed. At the very least you should be able to retrieve and deploy your TQ with only either hand.