Why do they keep stumbling over this part of the game with shout-heals, healing surges, and now auto-overnight healing? Instead of rendering non-magical healing a sore point of their game, and un-D&Dish when they're ostensibly trying to appeal to D&D players, why not just inject more magical healing into the game, like Kenzer did with Hackmaster 4E? It's not rocket surgery. Everyone else trying to make a D&D clone seems to get this detail right, without introducing suspension of disbelief howlers like healing surges.
If anything, with "shout-heals," healing surges, and so on, they finally brought all the HP mechanics in line with how they have narratively been explaining HP, while it's actually cleric spells named "cure serious wounds" and "potions of healing" that haven't been consistent with how HP were defined.
What you should be asking isn't "How does a warlord shout my wounds closed?" but rather "How does a cleric cure my "serious wounds" when I don't actually have any?" (a fighter with 1/99 HP and a fighter with 99/99 HP fight exactly the same, so clearly the one with 1 HP hasn't actually incurred any "serious wounds").
So should we get rid of healing potions and "cure ___ wounds" spells? No. You just have to use your imagination, which is the whole point of a game like D&D. Let's say you have 5/15 HP. How do the following things heal you? You drink a healing potion --> It relieves the pain of your minor cuts and bruises, contains an invigorating magical substance that keeps you fresh and alert, and tastes like strawberry. A cleric casts a healing spell on you --> All of your minor cuts and bruises magically disappear, and your straining muscles suddenly feel fresh and ready to move. A warlord shouts something quick, but inspirational --> Your ally's presence is so imposing, and his words so confident, that it reinvigorates your flagging morale and encourages you to push past your minor injuries. (I don't see why people have such trouble accepting that, in a fantasy world with wizards who control the elements and paladins who are so righteous that they gain minor divine magic,there won't be commanders who are so inspirational that they can encourage people to continue fighting beyond their pain threshold. It's a fantasy trope as much as anything else) You have to see HP as a combination of physical pain, morale, luck, skill, etc., but not serious injuries until you're knocked down.
Furthermore, the design goal for the DDN core rules are simplicity, simplicity, simplicity. Having convoluted systems for wounds are definitely right out, and even rules that require days of natural healing are needlessly complex because they violate the idea of what HP is.
Overnight healing of someone who has at least 1 HP is a great, intuitive, and simple system, but here's the thing. There's no reason why there can't be a "gritty realism" module that adds complexity to healing and wounds, requires longer periods of natural healing, etc. That would be a fantastic system that let many people play the game they want to play. It just shouldn't be the core, ground-level ruleset for HP and healing.