The main point is the conceptual plausibility. It is impossible to separate a premodern warrior from unarmed combat training. Even modern soldiers train in unarmed combat − especially for close quarters and build up (city) environments.
Regarding the UA 7 Fighter class description:
"Fighters learn the basics of ALL fighting styles" − including unarmed fighting styles.
I think this is a misleading truncation of the quote:
"Fighters rule many battlefields. Questing knights, royal champions, elite soldiers, and hardened mercenaries - as Fighters, they all share an unparalleled prowess with weapons and armor. And they are well acquainted with death, both meting it out and staring it defiantly in the face.
Fighters learn the basic of all combat styles. Every Fighter can swing an axe, fence with a rapier, wield a longsword or greatsword, and use a bow. Fighters master weapon techniques, allowing them to get the best use from a wide variety of weapons, and a well-equipped Fighter always has the right tool at hand for any combat situation. Likewise, a Fighter is adept with shields and every form of armor. Beyond that basic degree of familiarity, each Fighter specializes in certain styles of combat. Some concentrate on archery, some on fighting with two weapons at once, and some on augmenting their martial skills with magic."
This passage is not abstract or vague; the author(s) go into some detail about the Fighter's different abilities and training. And over and over again, the author(s) stress weapons, weapons, weapons. If they wanted to include unarmed combat as one of the core styles of the Fighter, they could have easily done so when they were listing the various specializations and techniques of the Fighter - and they did not do so.