At levels 1-3, yes I think it is. A good hit from an arrow or a wolf can take out a player. Above that characters tend to have enough features and HP to make dying outside of "Deadly++" encounters very rare.
However, I also houserule the way death works. I think the dying, death saves and attack rules are contradictory. Like...if you get crit while dying, it counts as two failed saves...but all hits while dying are auto-crits. So...if you get hit at all while dying it's two death saves lost. This feels like a rule written by someone who wanted to write "When you get hit while dying, it's insta death." but someone else told them that was too harsh.
So...
Everyone has negative Con Score "negative HP". "Zero" is always unconscious and stable. No death saves, no losing HP. However when you are at -1 HP or lower, you are "dying". Attacks against you are no longer auto-crits, they simply subtract their damage from your remaining negative HP, when you reach your maximum negative HP, you are dead-dead. However, each round while dying you get a "death save" to attempt to stabilize. The DC is 10+how far into the negatives you are. (so, if you have a Con of 12, and you're at -5, the DC for your Death Save is 15). If you fail your save, you lose 1 HP. If you make your save, you do not lose a HP that round.
First: This gives people more time. Rarely will you see a con score lower than 8.
Second: This maintains the feel that one good hit while you are dying could end you forever, as for the majority of the game, no con score will ever exceed 20.
Third: This streamlines the death rules. Dying is a progression towards death, not a whimsy of the dice.