Chaosmancer
Legend
I think I agree with you here. Especially since reducing a target to 0 HP doesn't immediately kill it. If you reduce a target to 0 HP, it should be unconscious and entering death saving throws anyway. All that would need to happen then is to have someone make a medicine check to stabilize the target to prevent it from dying.
But I find most of the time, myself included, DMs treat a target being reduced to 0 HP as insta-death. I used to remove the mini-fig from the board, before I realized that A) the body is still there and should be a potential obstacle (tripping hazard, cover, difficult terrain, etc.) and B) the players might not want to outright kill the target. I've begun leaving said mini-figs on the board until combat is over.
Cost-benefit analysis. Why are you making taking someone alive cost a second action? They will need to stabilize them within two rounds, or risk the 1 on the death save killing them. Meanwhile, just killing them requires nothing.
So, in a massive fight where the target goes down, they now have to decide if losing an action in the ongoing fight is worth saving this person for later. And yes, that can be neat narratively, but unless you are rolling death saves for all enemies, then you are setting things up where the smoother and easier path is to kill people. And DnD isn't a morality play, the more inconvenient doing something is, the less likely the players are going to be to do it.