I'm thinking that the change in taste of the water is the lack of dissolved gasses once you boil the water. Some people have tried aerating coffee and noticed a difference in flavor, but arguably that could be due to the sweetening of the coffee as it's cooled. The water you're brewing has been around how long? Surely the good tasting water you boiled the first time to make the tea was previously boiled in some point in the water cycle so as long as the water in your espresso machine boiler is not subject to contamination you should be good.

DaumierS wrote: On the other side, there are no machines that could use fresh just boiled once water.

HX machines brew with fresh water that's never been boiled (if you flush properly). It flows directly from line or tank to the grouphead, heated by the water in the boiler as it passes through the exchanger.

I suppose you could also say the same of an open kettle espresso machine. I used to use my La Peppina on a PID and never boiled the water, just brought it up to brew temp. I'd empty the kettle each day. I later simplified my routine to just plug in my La Peppina and bring the water in the kettle to a boil and then turn off the machine and prep my shot as I waited for the water to cool down to my desired pull temp. The La Peppina, not relying on the group to cool the water for the shot, took very little time to be ready to pull shots. When I used the PID I would sometimes leave it on weekend mornings for an hour or three, but there was little need for this.

I leave my GS3 on 24/7. I haven't noticed any change in the electric bill and I can have espresso any time I want. The folks at LM recommended leaving it run so I decided to make it so. Just like the other higher end systems, I think they are happier running.