Yes, you are merely reducing the bicarbonate via acidifying. To completely eliminate the bicarbonate ion species altogether requires that you acidify your water to pH 4.3, but most people choose to acidify their water to only around 5.4 - 5.7 pH. At ~5.4 pH nearly 10% of initial bicarbonate still remains.
This is something I don't understand.
Once dissolved, carbonate can exist in water in three different forms (aqueous carbon dioxide/carbonic acid, bicarbonate, and carbonate) depending on the pH of the water. The chart you posted shows this, and there is a similar chart on page 66 of Water. That chart also shows that below a pH of 4.3, all of the carbonate has converted to aqueous CO2/carbonic acid.
However, I don't think that it follows to say that you cannot eliminate all of the bicarbonate in the mash (whether through reactions between phosphates in the malt with calcium and magnesium that release hydrogen protons which react with dissolved carbonate to form water and CO2 gas or through the addition of acid with supplies the necessary hydrogen ions) without bringing the pH down to 4.3.
I can prepare a mash with distilled water (that contains no bicarbonate) and have the pH settle at 5.4. Similarly, I can prepare a mash with water that has 100 ppm bicarbonate and add enough acid to bring the pH to the same 5.4. In that second scenario, I have neutralized all the alkalinity that was due to the bicarbonate content of the strike water, haven't I eliminated all of the bicarbonate?
Or we talking about two different things here (the form in which carbonate exists in water given a particular pH vs. bicarbonate, residual alkalinity, and its effect on mash pH) or am I missing part of the larger picture?