Speaking as another artist/designer here...
...Leo had all the fine aesthetic instincts of an artichoke. Look at the Broadcaster/Telecaster guitar for an example. The headstock was designed to two criteria: saving wood and putting all the tuners on one side. Someone later said that there was barely room for the decal.
When Leo designed the Precision, he not only didn't improve on the Tele, he went backward: the amoeba pickguard is uglier than the one on the guitar.
Enter Freddie Tavares, who designed the Strat and split-coil P to Leo's specs (but I'll concentrate on the P here). All the disparate elements that comprised the characteristically Fender take-a-board-and-bolt-stuff-to-it-until-you're-done process have become integrated. A single pickguard now covers the routs, mounts the controls, and provides a place for the jack. And it's gracefully shaped to the contour of the body (something that Freddie didn't change) in such a way that it is one of the most natural-looking pickguards you can imagine. Compare with Leo's version, which randomly covers about half of the top, and still requires a separate piece for the controls and yet another piece for the jack! To give Leo credit, nobody knew how bass players would play the thing, so he was probably being careful: he didn't know whether players would use the thumb (as evidenced by the placement of the finger rest -- and note, there is at least one photo of Freddie, and accomplished musician, playing a first generation P with his thumb) or whether guitarists who took over the bass would play with a flatpick, which would require a guard to avoid scratching the finish on the top.
So Freddie, having successfully integrated the body elements,drew up a headstock based on the Strat, which he probably designed in the beginning to work in various formats. The result was that the total design looks like it came from the hand of single gifted person, which in fact is the case.
A lot of time has been wasted on the role that Paul Bigsby played in designing the Strat/2nd generation P headstock. The short answer is, "if Fender stole the idea, then why doesn't the Tele headstock look like that?" The long answer is, "given the flaws of the original headstock design, how many really cool designs can you come up with that incorporate 6-on-a-side tuners?" The answer to that is, not very many. People notice the superficial resemblance [and it's superficial only] and suddenly a conspiracy theory emerges. Sorry, I don't buy into any of that. Bigsby designed a pretty ugly guitar, if you ask me, and it was plastered all over with arm rests and doodads with Merle Travis' name and whatnot; the Tavares headstock was MUCH better from a design and manufacturing point of view. Or, to put it in simple terms, the Bigsby guitar looked to the past -- the Strat looked to the future.
Add to that the element of familiarity (noted above) and it was inevitable that the Fender headstock would look "right" if the instrument succeeded at all.
... There has been much speculation over the design for many years.
