Agreed. The kind of behavior I'm envisioning is that if I'm e.g. a young adult red dragon who just killed a human knight with a claw/claw routine, I might as well bite him in addition, instead of flying 30' to the next knight and trying to bite him. If the second knight is actively attacking me, that obviously changes my priorities.
Similar logic applies if I'm fighting disparate threats. If I just took down a guy who was swinging a giant axe at my head (GWM), I might double tap him even if there's a guy plinking at me with little arrows, because I want the axe guy to stay down. Basically anyone who proves to be a disproportionate threat should deserve a double-tap, IMO, regardless of healing, under PHB RAW for death saves. Personally I find the auto-revive on 20 annoying to me as a DM[1] so I only allow popups to 1 HP on natural 20s on Medicine checks, not death checks.
[1] It's annoying because it means I can't wait until after combat to roll death checks for all the unconscious monsters--I have to roll them during combat just in case someone revived enough to resume the fight. Too much hassle.