>truly pure water becomes acidic on exposure to air.

Correct, the carbonate is about impossible to avoid by distillation alone, you need to follow it with point-of-dispensing deionization to get a good blank. Though sometimes the older tradition of freshly boiling distilled stock might still be OK to get rid of CO2.

I just don't like stock any more, micro-organisms can change pH more than air and be more insidious.

But contact with the ever increasing concentration of CO2 in the air is not going to soon rival the amount of CO2 simply pressured into solution for mineral-free seltzer water. Way more carbonate ion in soluton as well as dissolved CO2 gas. Great to drink straight and not nearly as acidic as orange juice. Can nicely moderate the acidity of orange juice to end up with a refreshing lower-calorie orange soda too.

pH is very important but the huge difference is in buffer value where the titratable acidity of the carbonic acid in DI water is insignificant compared to the seltzer.

IOW when you take a sip of pure distilled water with no more carbonate than you get from the atmosphere and no other ions either, the pH of that sip takes on almost the exact pH your mouth had beforehand.

OTOH when you take a sip of seltzer which is simply pure carbonated water, that sip can make very prominent changes to the pH of your mouth (depending on how different your mouth was at the time).

I prefer to do both, repeatedly.

But not club soda which as the name implies has sodium like seltzer does not.

You can get even more carbonate buffer reserve into the water when you dissolve concentrated minerals like sodium bicarbonate and get true soda water instead of just dissolving CO2 gas under pressure, but for me there's too much sodium coming from too many directions already so I want my carbonation to come without sodium and not be a true "soda".