fishlips, a chemist will give a better explanation than I can... I'm only two steps ahead on the same road... where's RTR?
...but it helps to think of pH as a result in the three-way relationship between CO2, the alkalinity (carbonate/bicarbonate buffer or "KH"), and pH. You can't actually force those H+ protons that are being counted as the pH.
Our "soft" unbuffered water sinks to the low sixes because there's so little dissolved bicarbonate to neutralize the acids produced by metabolisms: respiration, nitrification etc. "Bio-acidification." So carbon dioxide remains as dissolved carbon dioxide and a little dissociated as carbonic acid. Nowhere for those H+ to go. The result is acidity, measured in pH.
The buffer just stabilizes at a certain endpoint. That endpoint pH rises as you add more carbonates/bicarbonates, til finally all the CO2 is bound up in the system, at about hmm. is it pH 8.3?
Alkaline water has less and less available CO2 for plants... adding CO2 "dissolves" the carbonates.
C'mon you chemists!