Lagostina press pistons have metal mesh filters. That implies that there will be fines to settle out in my coffee. Just get in the habit of not drinking that "last drop," but swill out the mug for cup #2.
I agree with you all = water quality matters. Good, bad or indifferent, you may be fortunate to have consistent water quality for the year.
I don't. My tap water comes off a melting mountain snowfield and glacier, about 5 miles west of my kitchen windows. Generally, I've never tasted better. I'm not fussy but there's a couple of gallons of my village water with me when I visit the city. Little too tasty, little too much chlorine, that I was used to, 20+ years ago.
The big May/June melt is about to start, the water will color up a little and the texture of ice cubes will change a lot.