If you look back to the 1960s and above, you'll find out there are so many famous guitar players like Jimi Hendrix, Jeff Beck, Eric Clapton, Stevie Ray Vaughn, and others, playing a Fender Stratocaster guitar across genres, like rock, blues, reggae, and more. Why did they use the Stratocaster? What aspects of the model make them interested on playing it?
The Stratocaster actually wasn't that popular in the '60s. If you watch the Woodstock movie, for example, you will see more Gibson guitars of all marques, and Fender basses in the main. In the '60s the Strat was almost entirely synonymous with surf rock and instrumental music, and couldn't reliably drive the front end of a tube amp in the same way that Gibson instruments could, which was the sound that a lot of guitarists were chasing in the latter half of the '60s. Hendrix is the exception, of course, but there is an almost super-human element to how he chased such a rich, thick tone from a Strat.
You mention some guitarists, but they probably all have different reasons for adopting the Strat, ultimately. Stevie Ray Vaughn didn't really surface until the '80s, so should probably be excluded from the list. Jimi Hendrix started using them when he moved to London in 1966, perhaps because in part he found the whammy bar to be a useful and expressive tool. It might just be the first guitar that he was given when he arrived, and quickly he became iconic for playing them reversed? He used Strats for stage work, but is photographed using many other instruments in the studio.
Jeff Beck used a Strat with the Jeff Beck group in the late '60s, but made far greater use of a couple of Les Pauls during the period. He used a Strat more from the mid-'70s onwards as it complimented his playing style more as he stopped using a pick and used the whammy as an expressive tool as well.
Eric Clapton possibly used one as a direct influence of Robbie Robertson of The Band. He was also moving away from Gibsons, which he used exclusively during the Cream era (with the exception of a Fender XII on 'Dance the Night Away'). Clapton took press reviews of his Cream period badly, with some claiming he was little more than taking a 'copy and paste' approach to earlier blues guitarist's licks and riffs. Perhaps for him the thinner, wirier Fender tone was a clear distinction from the meaty Gibson roar he had become synonymous with.
Generally speaking the Strat is ergonomic and quite comfortable to play for long periods, as long as you get on with the neck. Of the most popular guitars of the '60s, the Strat is more ergonomic than a Telecaster, lighter than a Les Paul and balanced more towards the body than the notoriously neck-heavy Gibson SG. Strats are also harder wearing. Watch the Rolling Stones' Gimmie Shelter film and you will see Gibsons haphazardly stacked against and resting on top of amps. Touring guitarists perhaps didn't baby their instruments so much back then, so Gibson headstocks got broken quite frequently. Stratocasters are modular, so broken parts can be quickly unbolted and replaced. Hendrix favoured some Strats and carried a cache of mostly sunburst, rosewood necked 'beater' Strats he would close a set with. There are photos and video evidence that suggests he typically threw the Strats into his amps to round off a concert, which would quickly break a Gibson.
I think a great deal of 60's appeal of the strat was that it had a double cutaway shape. Hendrix could never have played a single cutaway guitar like a Les Paul. (Although I have seen him play a SG.)
Also I do think the strat has a certain twang to it that lended itself greatly to the blues influenced rock'roll of the 60's. It was only when guys started wanting to get a lot heavier that the solid slab of wood known as a Les Paul became the norm.
A lot has to do with influence. And sound. People generally thought of an Ibanez as a piece of junk, until Steve Vai started endorsing it. The Strat is generally known as a Blues guitar because of the sound you can get out of it. There's always some exceptions (i.e. Dave Murray from Iron Maiden is a Strat player), but in general Strat players like the sound Clapton/Hendrix/SRV were able to achieve.
On the flip side, that big fat sound that Jimmy Page got out of a Les Paul is emulated by a lot of Hard Rock/Metal guys. It's a much more "ballsy" sound than the Strat. Joe Bonnamassa is one of the few Blues guys who play it, but his sound is more Blues Rock (a la Page).
Influence and sound (the masters play it and get that specific sound)but also because it has the most options of varied sounds. 5-way switch between 3 pick ups, you can go from jazz to rock to country. It's also one of the easiest instruments to customize. Add a humbucker pick up in 20 minutes and you have a brand new sound. The tremolo bar (whammy / Floyd Rose) is almost exclusively on Strats (or strat clones)and this is valuable for many types of music (surf, rockabilly, country, rock, hard rock and metal). An instrument that works well and is accepted by basically every type of guitar music - amazing in itself. Lastly, Fender has only seen success from two models of guitar: Stratocaster and Telecaster. The Tele has two pick ups, no tremolo (you can add one but its not easy)and is associated so strongly with country. The Strat has some come to mean "rock" it's the Model A Ford of guitars (and you can exchange parts from one to the other almost seamlessly).