D&D is an RPG... a role playing game. As a DM or a player, my tactics are determined by the personality of the character I am embodying at the moment. The knowledge, instincts, personality and goals of a character, whether PC or NPC, determine what they do when an enemy (or ally) fall.
As for whether D&D is deadly enough... while PCs in my games die, I think the question is flawed. PCs need to be challenged, but threat of death is not the only way to challenge them. If your combats all have to be life and death struggles where PCs barely survive, your PCs will not feel like heroes and it will get frustrating for players. If you feel combat is not deadly enough, I suggest you focus on adding other challenges to combats that PCs can lose even if their lives are not in significant jeopardy. For example, protecting something, stopping something from occurring, catching something before it escapes, deactivating something, capturing something, traveling through unusual environments, solving a strategic challenge (like an under dark rope bridge that is in the center of a 200 foot wide chasm with drow archers on both sides, or fighting your way out of a building that is collapsing/on fire).
Also consider that an individual encounter that depletes rest based resources is doing its job even if hps never drop that low. PCs that use too many resources in the first combat may find combat 3 or 4 before a rest more difficult. This requires there to be a time sensitivity for the PCs that limits how often they are willing to rest, but there are thousands of ways to achieve time sensitivity. One large time sensitive goal that overruns several adventures can do it with little maintanence (for example, recover the three MacGuffins from three sites in the next 20 days).