Well, it is true that with the higher pH buffering with borates you can add more acid to get the pH lower so move the TA lower as well, BUT it then takes longer and more aeration before you see the pH rise. The good news is that the pH remains low therefore making that aeration more efficient at driving off carbon dioxide. The bad news is that when you are done, it takes a lot more aeration to get the pH back up to a normal level since the greater pH buffering from the borates makes the pH more up more slowly.
So whether this is better or not is a matter of debate. Without the borates, the process of lowering TA is more obvious in that the pH is more easily seen to move so the "cycle" of acid and aeration while trying to keep the pH lower is more obvious AND at the end it is easier to get the pH back up without needing to add a base which would increase TA some. I think that for newbies it may be easier to lower the TA before adding borates so that they can see the pH changes from aeration more readily and recover (raise) the pH at the end using aeration alone. For more advanced users, doing the borates first should be fine and has the advantage of helping to keep the pH lower longer during the bulk of the acid/aeration process.
The addition of acid is what consumes carbonate alkalinity by converting carbonates to bicarbonates. The bicarbonate is then driven to the formation of aqueous CO2 in equilibrium with carbonic acid. So, when aeration occurs, CO2 is driven from solution and the reaction equilibrium shifts demanding the formation of more carbonic acid from bicarbonate and hydrogen. In all those reaction steps, hydrogen ions are consumed and therefore the pH ultimately rises.
The addition of acid consumes carbonate alkalinity mostly from converting bicarbonate to aqueous carbon dioxide (via carbonic acid) -- the second example you gave. Yes, there is some carbonate to bicarbonate conversion, but that's relatively minor because the amount of carbonate ions is relatively small. That is, what mostly happens is the following shift:
HCO
3- + H
+ ---> CO
2(aq) + H
2O
Bicarbonate Ion + Hydrogen Ion ---> Aqueous Carbon Dioxide + Water
So your explanation of carbon dioxide outgassing raising the pH is correct. I just wanted to point out which of the reactions was most dominant.
CO2 out gassing rates are, in part, pH dependent. Therefore if it requires more acid to lower the pH with the presence of additional solution buffering due to the borates, then that is what I mean by being "harder" to lower TA as it takes more acid to get to a lower pH. Perhaps instead of saying TA I should have specified "carbonate alkalinity" as borates do add to the total alkalinity of the solution (less so than carbonates but still noticeable at 50ppm).
The reason the CO
2 outgassing rate is pH dependent is simply due to the fact that at lower pH more of the carbonates in the water are in the form of aqueous carbon dioxide. That is, the aforementioned shift from bicarbonate to aqueous carbon dioxide is greater (more to the right) at lower pH. So the concentration of aqueous carbon dioxide is higher at lower pH so that drives the carbon dioxide out of the water faster since the amount of carbon dioxide in air is significantly lower. Doubling the amount of aqueous carbon dioxide in the water roughly doubles the rate of outgassing because the amount of carbon dioxide in air is much lower so the reverse reaction (transfer) rate is much smaller.
The addition of borates increases pH buffering (see
pH Buffer Capacity) so reduces the frequency of required acid addition, but it does not change the total amount of acid that needs to be added over time. You just add twice as much acid half as often, for example, for the net amount of acid per unit time being the same. This is because the pH buffering is the same in both directions -- on the way up from outgassing of CO
2 and on the way down from acid addition. So it takes the same amount of acid to get back to where one started.
Now the above is an over-simplification that ignores possible effects near the surface of the water in terms of mass transfer and ion transport. The greater pH buffering of the borates will make the transport layer somewhat thinner since the outgassing effects on water surface chemistry will be less self-extinguishing. That is, with less pH buffering without borates, carbon dioxide outgassing raises the pH of the water surface substantially and this shifts equilibrium to slow down the outgassing rate. With borates, the opposite happens. So while borates do provide significant advantages in the bulk pool water with respect to an overall slowdown in pH rise for that water, it may worse slightly the rate of outgassing itself. This is why to really have a net positive effect one lowers the TA level and/or targets a higher pH level since these directly lower the aqueous carbon dioxide concentration to lower the rate of CO
2 outgassing. These changes more than make up for whatever small increased outgas effect the borates may have at the water's surface.