If you use RO,
you will be able to get the pH stable,
without a controller.
I've used tapwater for 20+ years, growing dope on 2 continents. If I adjust a newly mixed tank's pH and leave the nutes in the tank, it stays put, without a controller.
However, when I start pumping the nutes into a rockwool media based system, the small amount of limestone powder remaining from RW manufacturing can cause pH to bump up, perhaps 0.1-0.2/day. Clearly, that's not the fault of the tapwater.
I've also seen root diseases, notably fungal probs, cause pH to jump significantly (+>0.5), even overnight. Not the fault of the tapwater, either.
Vinegar is a serious no-no in a hydroponic op. Put some vinegar in a sterilised clear container of plain water, cover or seal it and leave it at room temp for several days. You'll see cloudy gack form in the water. This will happen more quickly in non-chlorinated water. Why? Vinegar is a fermented product. Its acidity (~5%) at full strength stops it fermenting further in the bottle. Dilute it and the remaining yeast will often be able to reactivate. That's the cloudy gack- new yeast.
pHDown is made from inorganic chemicals which don't have the drawbacks of vinegar. It is available in a couple of formulations. It's usually a phosphoric acid solution, but some retailers sell phosphoric acid based pHDown for flowering plants and nitric acid based pHDown for vegging plants, though the P based type will do OK in all applications. On top of all that, pHDown is among the very cheapest solutions in a hydro shop. No real excuse not to use the right stuff.