High quality DI water is basically the same as distilled. A water softener is a form of ion exchange, where cations such as calcium, magnesium, etc are exchanged for sodium, whose salts are much more soluble so produces less scale. The same ion exchange resin used for softeners can be used to exchange hydrogen ions for the cations if it is regenerated with sulfuric acid instead of salt. I was responsible for a large DI unit (600 gpm) at a power plant and it produced water of extremely high quality. After passing through cation units, the water went through a vacuum degasifier to remove CO2, then through an anion unit (regenerated with sodium hydroxide), then though a mixed bed exchanger that removed traces of anions and cations.
Years ago Mercedes Benz used to recommend not using di water for cooling systems over concern for the affinity of di water to pick up oxygen, though I never understood their concern. As Pablo says, antifreeze has corrosion inhibitors and it is a non problem.
jldcol - pH 7 does mean 10-7 protons, but it also means 10-7 hydroxyl ions. H+OH=H2O. When the water goes through the cation units it produces acidic water, but this is neutralized going through the anion units, where sulfates, nitrates, and other anion units are replaced with the hydroxyl ions, so that you have the H+ and OH- combined....
Probably more info than anyone wants to know.