Household vinegar is fairly diluted at only 8%. It's acetic acid which is a weak acid, but with a pKa of 4.76 that's low enough below pool pH that it behaves much like a strong acid in terms of lowering the pH, but of course takes a lot more volume of it to move the pH since it's so diluted -- because of molecular weight differences, Muriatic Acid which is 31.45% Hydrochloric Acid is (31.45 * 60.05) / (8 * 36.46094) = 6.5 times more concentrated on a molar basis than household vinegar. Unlike Muriatic Acid that just leaves chloride ion leftover, Vinegar leaves acetate ion so an organic molecule. Though it doesn't react readily with chlorine, we generally don't add extra chemicals to the water that aren't needed.
[EDIT] In addition to lowering the pH, it would lower the TA in the same way as Muriatic Acid since the pKa is so low. Technically, it increases TA if you add enough of it though I'm not sure it would be that measurable -- the TA test measures chemicals that accept a proton down to a ph of around 4.5 so the acetate ion may be at least partially measured as TA. [END-EDIT]