Why so? It's all about framing a scene. Battles are largely battles of numbers, with lots of the action being abstracted until after the dice are rolled and the numbers accounted for. "Exhaustion" from a bar fight might easily be described as mental stress from concentrating on landing punches and avoiding hitting allies; thus, throwing a good punch or firing a straight shot could bolster one's confidence and recover that strain.
On the other side of the coin, if the GM wants to frame a scene wherein the players are tired from an extended trek out into a blasting desert or steaming jungle, he could simply state that the player's strain thresholds are lowered until they drink some water and get some rest. Doing the same thing during a battle might make sense if the players haven't slept in a long time or if they're tired from a long run, but on the regular it doesn't serve the narrative to just arbitrarily say "you can't recover strain from rolling well" without some kind of justification for that.
Strain is highly abstract, much more so than wounds. As such, strain is best used as a means of adding tangible flavor to different scenes by quantifying effects that otherwise don't fit easily into the rules (inclement weather, fear, lack of sleep, etc). It's not perfect, and it doesn't always immediately make sense, but with a little creativity and 3-dimensional thinking it shouldn't be that much of a problem, IMHO.
Your idea of mental stress from concentrating on fighting is nonsensical. It is an utterly bizarre concept divorced completely from reality.
The example ways of recovering strain are... resting, relaxing and eating. None of these have any parallel with shooting people in the face or having a light saber duel.
The recover strain on advantage mechanic stinks a little of something that got tacked on as it doesn't really match the rest of the book and how it describes what strain is. It certainly doesn't play out well by rewarding shooting a minion over a nemesis to recoup your strain and ends up feeling like many of the very worst video game fights where infinite minions spawn so the player can beat them up to recover their health.
It certainly feels dumb to recover from shock gloves or pushing yourself with extra maneuvers by spending your time using those maneuvers to take the most exhausting actions possible.