Healing surges also add a discomfort when dealing with healing character. The impression is that the healing capabilities of a character do not depend on how good the character is healing, but how many hit points the character being healed has.
For 5th edition we would like to see the healing surges removed, or at least replaced.
In the other hand, the bloodied value has been terrifically useful. It indicated that a character needs healing, or the monster is half dead. Is very easy to imagine the monster bleeding, or with all the body covered by blood. Even though is a little weird to talk about bloodied value for creatures such as undead or constructs, maybe it is best for those creatures to be immune to effect caused by them being bloodied, because they wouldn’t bleed.
Healing must be magical unless applied using the Heal skill. It is difficult to imagine someone dying and unconscious to wake up, stand up and fight, after someone yell some inspiring words. It is difficult to imagine someone getting healed because he suddenly takes a second breath (second wind) or a sudden moment of motivation. That kind of situation can work best with temporary hit points or even bonus to attack or damage, but not being magically healed.