The browser does store the text in the text area, but the text area disappears when you reload the page because you need to click a button that adds that element to the page.

Well that's the page's fault, we used to call that "breaking the back button / history". And apparently not enough people think that was big enough of a deal to stop doing it. Unfortunately.

And even Opera tried to keep that too, at least in many situations, to keep the history an actual history and you'd switch through snapshots of the DOM+state--at least that's what it felt like, I'm not sure that's what it really did, but I guess it helps with speed, too. A webpage generally isn't supposed to move or change at all unless you're interacting with it, so really after it's rendered, flipping through history or tabs should be instant, even on an old machine because it's just bitmaps, really. I remember a while ago there was an article here that sort of explained why this couldn't be done or didn't work for some reason, but it was a tradeoff to get some feature that, given the option no one in their right mind would trade for instant history and tab navigation.

Even if it's the page's fault, you still lose your text. At that point, you don't really care who to get angry at, do you? Which is why I always disable backspace for back navigation.