To me it boils down to this:
1. It's a simple design that just works.
2. Because of this, It was a huge success, becoming common and often-imitated.
3. Because of THIS, it has become the standard, and feels familiar and "right".
To me Leo Fender's main merit as an industrial designer was not having genious-level artistic vision and foresight, like some people seem to think.
To me what's greatest about him was his practical nature and urge to simplify. The Telecaster wasn't a thing of classic beauty when it was invented. That's what we think of it of it now!
It was, however, a radical new way of making guitars, with every detail being as simple as possible to get the most efficiency out of the industrial process of the time. If you compare it to the later, more refined Stratocaster, you can see it was designed by an engineer and not a musician: it's all right angles, flat shapes and bolt-on construction so it could be made cheaply and quickly by unskilled labor.
And hey, it worked.
It's because Leo could make a good innovative product cheap enough for the masses, not unlike Henry Ford, that he was able to get his investment back and keep on trying crazy new stuff like an electric bass. But not necessarely, as many people seem to forget nowadays, because his first design was such a lovingly crafted and artistically conceived masterwork that the whole world had to take notice. It wasn't. It became beautiful and classic to us later, because it worked so well.
And all that goes for the headstock design, IMO. Which, as some have pointed out, it's not even the original one! It's a refinement, that came a bit later and was much more popular.
It's simple, it's very functional, and it became the norm for very practical reasons. And that plays a big part on why it's so beautiful to us fifty-some years later.
Familiarity is a bigger factor than many people realize when deciding what they like and what they don't. Why do you think advertisement for products and services and radio/tv exposure for mainstream artists work so well? "I know that one!" is halfway there to "I love that one!".
We have no one even slightly familiar with industrial design--or design in general?
I studied three years of product design in college before changing my mind and studying five more years of graphic design and just recently graduating in it. So I guess I'm slightly familiar or more.
Nothing "just looks right".
I wouldn't say that. To me "looking just right" is a natural psychological consequence of any design that was such a big success it has become a standard.
This can apply to generic things like a doorhandle or a faucet, or any given "design classics", from a Fender Stratocaster to a Coca-Cola bottle to a simple Bic pen.
They can indeed "look just right" exactly because those shapes have proved so long-lasting that they've become ingrained in our culture, to the point of being the very first things a lot of people picture in their minds when they think of "guitar", "soda bottle" or "pen".
Sorry about the design geekery, couldn't resist! To anyone even vaguely interested in this kind of thing, I suggest taking a look at Donald Norman's
The Design of Everyday Things. It's a very easy, entertaining, and enlightening read.