They're nifty little pumps, but they're absolutely not "distilled water" in the sense that you're imagining - It's not steaming up, condensing, and dripping. It's steaming up, pushing a bunch of liquid water up a small tube, and then burping the whole payload onto the coffee, including any and all impurities that are already in the water.
Example video here: https://www.youtube.com/watch?v=xV8vZqHd0ao
They're used lots on budget aquaponics/hydroponics/aeroponics setups because they can push water up surprising heights with nothing but a cheap aquarium air pump, or - in the case of a drip coffee machine - a cheap heating element.
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All of that said - you're still running that water through ground coffee and then a literal filter. I'd not be surprised in the slightest to find it also removes a lot of things.
What could be better than that?
How about a drip coffee maker? A drip coffee maker creates little steam explosions to push water vapor to the top of the unit where it condenses and "drips" down over the coffee.
Since steam is being produced, in essence, distilled water is being used which if I understand the physics correctly, should be relatively free of metals.