If you pay attention to how short rests are worded, then there is no need to change to wording of the second wind ability, it works as intended as written.
Nope.
From How to Play:
Short Rest
A short rest is
a period of downtime,
at least 1 hour long,
during which you catch your breath,
eat, drink, and clean and bind wounds.
Where on earth do you get the impression that you there can't be two consecutive periods of downtime, concatenated one shortly after another?
It certainly isn't in the rules as written. If it is, tell us how long exactly it is until you can take another short rest after the first one, because that is a pertinent rules tidbit which would affect many tables. You can't, because there is no such rule.
And judging by Mearls' response to how to deal with multiple short rests (DM tell players they are being boring), it's not there in the final rules, either. Or maybe someone else wrote it in the final rules while he's not aware of it (we can always hope), in which case it becomes a matter of, why. Because if you happen to get into a combat immediately after a short rest, which often happens by design, since players are fresh and they charge in, then you need a solid rule to tell them no, you can't take another short rest after that combat. Telling players they can't do "encounter nova" guerilla strikes just because the fighter has Second Wind seems like an even poorer choice than leaving this serious flaw in the game in there.
The real solution here is for it to use HD or Temp HP, obviously. Temp HP would be instantly better because the ability is called stamina, and like an adrenalin rush, dissipates after 5 minutes.
Simulationist rules are simply better. They make the action easier to understand without a veneer of gamey terminology to confuse people and expect them to come up with weird explanations for things that should be simple to understand.
