The energy input to render all that liquid water to steam and then cool it again is orders of magnitude greater than just bringing it to the boil and cooling.
Distilling takes a lot more energy. Once water hits boiling point the energy to turn it to steam is far more than heating it up 1°C when it isn’t boiling.
I remember having a little carbon block drink bottle at one point, which claimed to filter out the larger of bacteria (maybe it was viruses - they’re a lot larger, aren’t they?) - I wonder if they’re effective (not that we really consider throwing away carbon blocks progress!)
Actually doing the math, each kg of water takes about 4.2 kilojoules to heat by one degree, or 336kJ to heat from 20C to 100C.
Each kg of boiling water (already at 100C) takes about 2250 kJ to turn to steam. Pretty wild difference because it takes a lot of energy to break the hydrogen bonds.
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