To Death Save or not to Death Save, that is the question

When I read about the Death Saves I didn't like it. It seemed characters would be impossible to kill, which seemed unrealistic, and the threat of death is a big part of low-level play I like. Then we had a character go down in the middle of battle, the Cleric of all people, and were were mostly playing rules as written, so I looked up the rule:

Death Saving Throws
Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving throw, to determine whether you creep closer to death or hang onto life. Unlike other saving throws, this one isn’t tied to any ability score. You are in the hands of fate now, aided only by spells and features that improve your chances of succeeding on a saving throw.

Roll a d20. If the roll is 10 or higher, you succeed. Otherwise, you fail. A success or failure has no effect by itself. On your third success, you become stable (see below). On your third failure, you die. The successes and failures don't need to be consecutive; keep track of both until you collect three of a kind. The number of both is reset to zero when you regain any hit points or become stable.

He failed two times, and on the third round the Bard healed him making a third roll unnecessary. It felt like a cheat. The guy was dead, but those are the rules so I let him live to fight another day.

Then later I talked to the Colonel and the Death Saves came up. It wasn't his character that went down but I don't think that would have changed his opinion. He really liked the way it worked. He fought in Iraq and said you had guys go down and you had a certain amount of time to treat them or they were gonna die. That meant one of their fellows had to stop fighting and help the injured person if a medic wasn't immediately available. Suddenly the combat had two less guns which could be very bad. They would stabilize the injured and send them off to a M*A*S*H unit to get proper attention later. Anyway he felt the game modeled the tactical situation pretty well, so I've been rethinking my dislike of the Death Saves as my life of technical writing has not really put me into a lot of combat situations but it has taught me to trust subject matter experts.

The one catch to all this is it makes a total party kill a bit more likely as you lose a combatant, even for a round, can really turn the tide of battle.