Guitars aren't complicated machines, and there's no special reason that a Squier shouldn't stay reasonably in tune, as long as it's set up properly. However, factory-produced guitars almost never come properly set up or with a well cut nut. The nut in particular is important to tuning stability, especially when using a vibrato system.
There's a lot of difference between Bigsby, strat, Floyd Rose, and Jazzmaster systems, but none of them is indispensable. Many people go their whole lives without ever owning a guitar with a "tremelo"/vibrato.
There are some techniques you can't implement without one. On the other hand, on a hard tail you can do other things like bending one string in a double stop and not have the other go out of tune. If you break a string you can keep playing until the end of the song without being completely out of tune. You'll probably find that you have longer sustain. Palm muting is easier.
tl;dr go ahead and buy a hard tail, you won't regret it.
In effect, is it really that different to a fine? It seems to have a couple of advantages, though: it's easier to collect, and it's proportional, so a person who can afford a fancy luxury car pays more than someone in an old banger, without the complexity of having to evaluate their income and savings.