In a nutshell: Why the alk lowering process works

[waterbear]

The only real advantage to having a higher TA is when you are using stabilized chlorine which is acidic. The higher TA (which will eventually get depleted) will keep causing the pH to drift upward and help stabilize the pH. With bleach or any other unstabilized chlorine running a lower TA will minimize your acid usage needed to maintain pH.

Edit: Carl is correct that there is no reason to worry about TA in a vinyl pool as long as your calcium levels are not too high. You might need to add acid more freqently if you are using bleach but there really aren't any other negatives. If the calcium levels are high then the combination of high TA and high calcium can lead to scaling or clouding of the water, especially if you let your pH get out of line and rise.