Hey Gil, maybe the high E strings were just old, grotty, oxidised and generally worn on those "pawn shop special" guitars? Whammies DO bust strings (not JUST high Es either

...) at a reasonable pace if used violently. (But) you should still be able to get a decent amount of playing time out of a set of strings. I find that [the reason for the strings breaking more with a whammy] isn't really the sudden tension variation in the strings (which are designed to take a lot higher load than standard guitar tuning anyway), but the general weakening of the strings due to the constant bending back and forth of each string right at that point (where they touch the saddles) causing metal fatigue over time. If the strings couldn't handle the tension without weakening them first, they would break the first time you raised the whammy all the way... 💡
If you use the trem just for a little bit of subtle Pink Floyd style vibrato every now and then, I can't imagine you going through high E strings much faster than with a non-trem guitar... you need to use the bar pretty violently (quickly changing the angle where the strings meet the saddles) if you really want to break strings fast...
I suppose my point is that having a guitar with a trem system doesn't mean you will break a lot of strings by default... If you don't use the trem it won't break strings all by itself! It's still good to have the option to use it and forego a little bit of string life IMO...
My Les Paul doesn't go through strings anywhere near as fast as my strat or Ibanez, but the Gibson also has chunky strings to accentuate that guitar's ballsyness, and I also don't play it anywhere near as much as either of the other guitars (due to a whammy becoming more and more incorporated in my playing...)
My thoughts are like this: a guitar without a whammy is kinda like a piano, very nice for rhythm etc but not as lyrical as a violin - which a whammy frees you to be able to achieve (that kind of lyrical singing quality)... When I play my les Paul I almost feel like an important part of the instrument is missing. IMO a Floyd Rose equipped guitar (like an Ibanez JEM) could almost be considered in a different catagory of instrument (kinda like how there are harpsichords and pianos - although with the same keyboard layout... they are still considered very different instruments) due to the totally different approach needed to get the most out of each... I feel that there are so many different types of electric guitars out there with different techniques and approaches needed to play them all, that the simple name "electric guitar" is perhaps outdated as an offical catch-all name for them all. The electric guitar is so new an instrument (historically) that perhaps we need to catch up (naming-wise) with how it is evolving... Maybe I'm crazy, I dunno.
ANYWAY, sort of back on topic...
Both Bigsby and traditional Strat type trem systems were only really designed (back in the day - pre 80's shred

) to provide gentle vibrato effects... nothing too crazy - kinda like Hank Marvin from The Shadows.
Hendrix took the traditional strat trem about as far as you can really - and his Live at Woodstock DVD omitted
lots of tuning up he did between EVERY song...

(he called it the tune-up blues and kept apologising to the audience for having to tune so much

)
Jeff Beck uses his traditional strat trem to do more subtle nuances and stuff (rarely much more than bending a tone in pitch), only occasionally depressing it all the way - usually at the end of a song, where it doesn't matter if it sends the guitar out of tune. Stevie Ray Vaughan didn't use the trem a MASSIVE amount either, and when he did, it
did go pretty damn out of tune (he did smack the guitar on the stage and use the bar with his foot though

).
Players like Dave Gilmour, Jeff Beck, SRV, Hendrix etc really knew/know the limits of the strat trem and know when and how much they can get away with using it so they stay reasonably in tune - and give the impression that they can use it however much they like (which really isn't the case)... It certainly fooled me when I was young and impressionable!

I thought (before I had a proper strat) that Fender's traditional trems could be used in a far more crazy way than perhaps they really could... (I never saw the footage of Jimi madly re-tuning between nearly every song during live gigs...)
Basically, if you want to do crazy whammying consistently and in-tune like Satch/Vai/Eddie etc, you NEED a Floyd Rose or similar. Locking nuts are FANTASTIC (until you break a string and its a b**** to change

). You can just leave the screws undone on it (less of a hassle) when you're not gonna be playing any squealin' harmonic divebombs for a while...
You CAN technically set up a strat to work with the old style trem very nicely, but it really takes some doing (and a lot of luck), and all the painstaking tweaking goes out the window when you put on a slightly different gauge set of strings...
It took me a LONG time to get my strat to where I thought it was as good as it could be... Lots of experimenting with different custom string gauges, different setups of the bridge... it was a total bastard to get working nicely.
I'm basically locked into using the same gauge of strings for it now, cause I'm scared I'd set off it's special equalibrium and never get it back quite right if I changed anything about it now...
Making sure the string saddles on the bridge are really smooth with no badly machined jaggy bits lets strings last a hell of a lot longer (part of why cheap guitars and whammies are sometimes a bad idea). Putting some form of lube on the saddle helps keep the breakage under control too (sorry for that sounding like a line from Breakback Mountain

). Graphite works nicely if you don't want it becoming all greasy and sticky...
On that note (not a pleasant one - sorry), I'll end my randomish late night guitar rant.