I'm glad someone brought up the CLW wand [or the equally fun Wand of Lesser Vigor for 'short rest healing'].
When the game became about "how to use magic to get around the realism of it taking a long time to heal" ... it was easier just to make healing easier instead of creating a whole system of "five minute adventure day" and hospital on a sticks.
We question how someone can 'bounce back' from having an Axe stuck in them and recover from unconciousness and being bloodied ... but the fact that they fight JUST as effectively at 1 hp as when they are at full [and in some cases, more effectively for, say, a Dragonborn] which has been around in EVERY edition of D&D is perfectly fine?
I guess if they update to an even newer edition, they should just eliminate martial completely, because it isn't as realistic as unexplained, undefined magic making the wound that doesn't seem to have any noticeable effect [other than bloodied related effects] go away in an undefined way. There is no missing body parts, no permanent disabilities, etc ... unless they are specifically introduced through some sort of lasting effect, like a disease. So, already the wounds are obviously not THAT bad. There is a risk of death, but it isn't necessarily someone holding their guts in during the fight.
Healing surges are actually a realistic mechanic, as much as people may not like it. The idea that someone can be infinitely healed, without rest, as long as you have the available magic, seems to ignore how much punishment a person can take. If this represents real wounds, even being fully "healed" of the wounds wouldn't account for the mental toll that the pain they accumulated would give them. They could take thousands of damage in the day, but as long as there are charges remaining in the wand, they are fine. With healing surges at least, there appears to be an internal limit to the ammount of healing remaining.
Also, not there are specifically magical forms of healing, like Lay on Hands and the Cure Light Wounds, etc... which provide "external" forms of healing, which do not come from the healing surge. Heck, the Cleric's ability is basically the same as the Warlord. It is a prayer, some kind words, doesn't necessarily mean it's invoking divine intervention.
It's not that warlord's word is magic ... it's that the cleric's isn't as magical as some of his other powers. Not all of the cleric's power is drawn from divine sources, some of it is good old fashioned martial might and some inspiration to the group to boot.