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Distilling is different from just boiling, in the sort of context we''re talking about you're just getting water up to boiling in a container to kill pathogens, not collecting the steam that evaporates off of it to condense back into water to drink.
And in a lot of survival situations you'd be lucky to have something to boil water with, let alone construct a still.
To their credit, yes, theoretically boiling water will concentrate things like heavy metals. You're just not going to be able to get it hot enough to evaporate stuff like lead or mercury, all of the water will boil off and your pot will melt long before that if you can even reach the sorts of temperatures needed (you probably wouldn't be able to, at least not without constructing some additional infrastructure, and if you're capable of that odds are you're pretty much set for this kind of situation and not need to be reading anything in this thread for advice)
In practice, you're just not going to be boiling water hot or long enough for that to really matter. You really only need to get it up to boiling for an instant then you can take it off the heat (and arguably it's probably safe at some point before it reaches boiling, but unless you have a thermometer, stopwatch, and some tables to consult about pasteurization, it's a lot easier to just watch for a boil.) Go put a few cups of water in a pot on the stove and get it up to boiling, how much did the water level change? Probably not all that much, you're not doing much to concentrate whatever's in there.
You have maybe a week you can go without water under absolutely ideal conditions, more realistically you probably have about 3-5 days, or even a few hours if it's hot and you're exerting yourself. Most toxins you're going to find in water aren't going to kill you in that sort of time frame, they're more likely to be something that will add to your lifetime exposure and bioaccumulation and cause issues for you sometime down the road, maybe years or decades later.
And if the concentration of whatever you're concerned about is high enough to cause more immediate issues, odds are that you're kind of fucked either way, and the tiny bit of concentration that happens from boiling isn't going to be a major factor. You'd probably get sick regardless, you're just trading one issue for another- dying of dehydration in a couple days, or dying of poison in a couple days.
And some more volatile chemicals might evaporate off in the boiling process, let's say that for some reason there's a bunch of acetone in the water (picked that for no other reason than because I happen to be looking at a can of it on a shelf in my basement while I'm writing this) acetone boils at 132.8°f (56c) so by the time the water reaches boiling all or most of that acetone has already evaporated.