First, let me explain the experience I'm going for. I prefer natural healing along the lines of 3e (and no, I'm not including
wand of cure light wounds in that--I'm talking about how fast people heal without magic). I hope there is a healing module to support that, by some means other than changing the duration of short and long rests (because that doesn't really accomplish it and it has the added problem of screwing up other things like spell slot recovery that I don't want moved to a weekly basis).
I also am not really interested in any experience where combat time and non-combat time are somehow treated differently. I don't like effects that allow you to do things when you are fighting, but not when you aren't. You end up with the bag of rats, or having fist fights with your buddies to activate your abilities. I understand that some people play D&D in a more narrative style and those issues don't come up, but I play it simulationist and I need there to be a mechanical reason such things won't happen.
I treat hit points in such a way that I'm okay with small amounts of non-magical healing or buffering, but not enough to go from 0 to max in a day or so. (I'm obviously not using the default of fully healing overnight.)
From that perspective, I'll try to explain why Second Wind doesn't work, as written.
1. If a fighter can self-heal 1d10+level hp between hour long short rests, and short rests aren't limited, he can heal himself back to full hp in a day or less (usually
much less), without any need for overnight healing. This needs to be somehow addressed in combination with slower healing modules, or fighters have a unique ability
to spit on the slower healing module. "Haha slower healing, take
Second Wind!"
2. Even without the game experience I'm going for, it ends up putting wounded fighters into an exclusive situation where they can benefit from multiple short rests in a row, while other classes (unless something major has changed) can't. That can be annoying in play. "Okay guys, we should probably rest for 4 hours so the fighter is back to full hp," or "hey guys, can we take another short rest? My fighter needs a bit more healing."
I'm going to guess that this is exactly the case. Notice that the Second Wind healing amount is the figher's hit die. I imagine it was just simplified for the Starter Set and the pregens.
Actually it is 1d10+level hp. HD is 1d10+Con mod.