OK, on a mechanical/balance level, range is increased because as characters level, they can gain additional movement modes and faster speeds and things: in play-testing, it was found that there was little-to-nothing melee characters could do to keep up with ranged characters, since far too often they were unable to get adjacent.
Legend and Fluff
For fluff, Legend doesn’t like dictating to you why your mechanics are the way they are. All the fluff in Legend is a suggestion at best, and the system heavily encourages refluffing to match your character. So there’s nothing in the book directly that explains why the reach increases; you’re free to call it what you like.
For example, if you wanted a character with Dhalsim-esque stretchy punches or anime-inspired air pressure slashes, you could just say that’s how your melee reach extends. Of course, those are really niche characters that don’t fit everyone.
A High-level Mundane Warrior in Legend
The “suggested” fluff for it, assuming that you’re not super-stretchy and don’t care for dubious applications of meteorology, is that your melee reach represents your “area of control.” It is the area in which you can operate safely, i.e. not triggering attacks of opportunity for your lunges and the like.
Basically, in the same way that every creature occupies a 5-ft square, despite not having a 5 ft2 footprint, your increasing reach represents the idea that you are moving around – even outside of your square, now – but you’re doing so within an area that you control. The control isn’t as strong as your own space (i.e. you cannot keep others out), but it’s enough to prevent attacks of opportunity or other things that might trigger on movement.
A move action, then, becomes less about actual movement, and more about moving this area that you control. You’ve carved out a little breathing room for yourself in the middle of the battle, but if you need to deal with things outside that space you’ve gotta take some risks.
I am not a martial artist, but I have been told that this idea does represent, in a fairly abstract way, how actual combats take place. The increasing reach is important in Legend for mechanical reasons, but that does not mean it has to be swallowed as a “necessary evil” as far as loss of simulation goes (unlike, say, Legend’s flight rules, which are unabashedly “3D flight is a nightmare to run and is way too large an advantage, so we’re going to abstract it heavily to eliminate that even though you do lose some verisimilitude”).
Legend, Power Expectations, and Leveling
The other thing to keep in mind is that Legend has embraced the idea of massive growth as one levels. Legend did not approach “linear warriors, quadratic wizards” by linearizing the mages (though they have, of course, been nerfed compared to 3.5’s insanity). At high levels, all characters must be routinely ignoring the limitations of the human body, and frequently bending, at least, the laws of physics. That includes the martial, “mundane” characters. This is usually represented by various forms of Badass Normal, Super Secret Training, whatever. Stuff you see in Batman comics and various anime.
It’s not that Legend embraces any kind of “anime style” so much as the fact that anime is one of the few mediums where you frequently see mundane characters with powers and abilities on par with what is expected of a high-level Legend character. The melee reach isn’t the only thing: take a look at what you can do with high-ish Acrobatics and Athletics checks (e.g., under things you can climb, there’s a DC for “raindrops. The falling kind.”).
This isn’t for everyone, and that’s why Legend has narrative-based leveling – if you don’t want the characters to reach those kinds of power, simply don’t have them level that high. The game is designed so that levels 1-5, roughly, can represent a fairly gritty medieval fantasy game, 6-10 are more like fantasy heroes and the like, and beyond that gets into ever more over-the-top power, approaching on material frequently associated with gods.