I find this a chicken-or-egg dilemma then.
Is the dwarf hardy because it has second wind, or does it have second wind because its hardy? Which comes first, the mechanics or the fluff? D&D has traditionally written from a place of fluff first, mechanics support it. Your proposing that the mechanics come first, and then you can hang whatever fluff you want on it. That is a very radically different way of doing things.
Lets try an experiment. I have a monster I designed years ago (2008) for my 4e game. I will post its stat-block and nothing else. Describe to me what that monster is. (Hint: Dahlia is the creature's name, not type)
[sblock]Dahlia Level 1 Elite Skirmisher
Tiny fey beast XP 200 each
Initiative +6 Senses Perception +2; low-light vision
HP 40; Bloodied 20
AC 20; Fortitude 15, Reflex 22, Will 17
Saving Throws +2
Action Points 1
Speed 6
Claw (standard; at-will)
+3 vs. AC. 1d4+1
Eyebite (Standard; recharge 56) Arcane, Charm, Psychic
Ranged 10; +4 vs. Will. 1d6+3 psychic damage and you are invisible to the target until the start of your next turn.
Undeniable Beauty (immediate interrupt, when Dahlia is targeted by a melee attack; at will)
+ 3 vs. Will against the attacker; the attacker must target a different creature or end its attack.
Lure of the Wild (standard; recharge
)
Ranged 10; + 3 vs. Will. The target is pulled 5 squares and is dazed (save ends).
Step Through the Mists (move; encounter)
Dahlia teleports up to 3 squares.
Alignment Good Languages Common, Elven
Skills Acrobatics +9, Athletics +5, Stealth +9
Str 6 (–2) Dex 18 (+4) Wis 10 (+0)
Con 12 (+1) Int 14 (+2) Cha 12 (+1)
Equipment +1 amulet [/sblock]
Here is some perfectly good mechanics. Weave me a story.