One thing to consider in the likelihood of death in a D&D game is how well the players play together. That isn't always obvious, not even in my home campaign with a group that is playing together for 15+ years. In a RPG club group coherence is really an issue and it is more likely that everybody plays his character selfishly rather than trying to help others. For example at one point in a big battle my paladin was at 0 hitpoints, unconscious and dying. The group's cleric was in range. But his warhorse had also been knocked unconscious. So he decided to heal his horse rather than healing me, the group's second healer. Yeah, right.

As the DM has a penchant for deadly encounters, people getting knocked unconscious in battle happens all the time. In one fight the barbarian was down 4 times, and my paladin was down 3 times. That also explains why somebody being unconscious doesn't necessarily result in an immediate "we must save him" reflex, it occurs just too often.

If something happens frequently enough, it is worth looking at the possible outcomes and their statistical probability. The 5th edition system of death saves is simple enough, you roll an unmodified death saving throw every round until you accumulate either 3 successes and stabilize, or 3 failures and die. It is slightly complicated by critical successes and failures, a critical success not only stabilizing you but also giving you back 1 hit point, while a critical failure counting a two failures.  So somebody better at math than me calculated that the probability of surviving when unconscious without external help or hindrance is 59.5125%. That is clearly weighted in favor of the player, but still a 40% chance of dying is significant.

So in this case me and the cleric got hit at the same time by an area attack and both got knocked out. One round passed and we both failed our first death save. Nobody else had the time to stabilize us. The next round came and by a fluke of fate we both rolled a critical failure on our second death save, so be both died. The DM clearly hadn't wanted this. One of the subtleties of the death save system is that the DM can't fudge dice, because it is the players who roll the saves. So the DM was forced to pull out the big guns, the deus ex machina device of having the cavalry arrive and save the group from a total party kill. In this case we even were offered a resurrection, but the DM asked whether we wanted that "out of character". The cleric accepted, I declined.

It isn't just that I am philosophically inclined to accept the results of random bad (or good) luck in a role-playing game as being a third actor besides the DM and the players. I also was happy enough to get rid of my paladin and roll a new character instead. As I mentioned above, the group coherence isn't very good, and I had designed the paladin to be a very selfless character, tanking and healing for the benefit of the group, while not having a lot of opportunity to shine with big damage. My paladin only dealt decent damage on a critical hit, because he had an ability that allowed him to add dice to damage after seeing the result, and a critical hit doubles those dice. But otherwise his damage was never impressive, and he ended up spending a lot of rounds in combat trying to heal or save other people. Playing a character like that in a selfish group isn't all that much fun.

It also turned out that I had overestimated the efficiency of armor in 5th edition. Unlike 4th edition, in 5E even spell attacks are rolled against armor class, so I had thought that with a high enough armor class I would survive much longer. Reality turned out to be much different: First of all not all spells and attacks work with attack rolls, but sometimes they are based on saving throws, and armor doesn't help with that. And then even in melee, if I was twice as hard to hit as another character, but ended up tanking in the frontline and got attacked more than twice as often, I still ended up taking more damage than others.

In addition the group I am in curiously had only melee characters. Even the wizard took the bladesinger subclass and is dealing most of his damage in melee, while using his spells to protect himself. So the new character I made is a warlock with a ranged spell attack specialization. I will see how that works out in the next session.

The lesson learned as a DM is that one shouldn't be afraid of knocking player characters to 0 hitpoints. What happened to me, a failed first death save followed by a critical failure on the second, only has a 2.25% chance of happening. Other than extremely massive damage this is the fastest way a character can die, and it takes two rounds. So as long as the rest of the group has the means of stabilizing a dying character (which is easy enough with healing kits and potions even in the absence of healing spells), and is willing to do so, death shouldn't happen all that often. It is very much in the range for "death should be possible, but not frequent" philosophy of my games.