It is correct that Alkalinity acts as a buffer to prevent pH from crashing down.
What's important to understand is what chemicals are actually behind "TA". The main contributer to TA are carbonates in the water (we add baking soda to raise TA, aka sodium bicarbonate). This builds up a carbonate buffer system. So far so good. But at pool pH, these carbonates are mainly dissolved CO2 in the water.The pool is oversaturated with CO2 that wants to outgas into the atmosphere. Pretty much like in a soda bottle - when opening the bottle, CO2 escapes making the water taste less acidic, i.e. raising the pH.
You want some TA to protect pH from crashing down, but not too much to minimise pH rise.
When keeping TA somewhere around 70, the pH at which dissolved CO2 is in equilibrium with the atmospheric CO2 is around 8.
Many (and you seem to be one of them) are able to stabilise pH in the 7.8-8.0 region by maintaining TA somewhere around 60-80.
Just don't let TA drop below 50. When that happens (but not earlier), raise it with baking soda back to around 70.
The chlorination cycle with an SWG is pH neutral. Generating chlorine in the cell raises the pH initially. But dissolving the produced chlorine gas into the water is an acidic process, and so are the processes "using" chlorine (like UV killing FC or FC killing algae). Once FC is is back to where it was before being created by the SWG, pH is also back down to where it was. The cycle is pH neutral.
But in parallel to all this, CO2 keeps outgassing and rises pH in the process (the higher TA and the lower pH, the faster the outgassing and the pH rise).
The myth about SWGs raising pH originates from people's experiences who change from Trichlor pucks to an SWG. Chlorinating with trichlor is very acidic and compensates the pH-rise from CO2 outgassing. It actually overcompensates the rise, resulting in TA dropping down, until TA needs needs to be raised again. That's where the "traditional" recommendation to keep TA around 100-120 comes from - with Trichlor that's quite important.
When changing from Trichlor to an SWG, the pH-rise from CO2 outgassing gets no longer hidden by Trichlor, and adding muriatic acid becomes necessary - until TA is low enough to stabilise the pH rise.
Because pH crashing down with an SWG is not a risk (as it is with Trichlor that constantly keeps pulling pH and TA down), TA can be allowed to be maintained lower with an SWG.
Depending on TA of the fill water, TA can rise again with fill water additions to replace evaporation losses, and pH might start to rise again. Then you'll automatically start adding acid again and you'll eventually get back to your equilibrium TA.
Everything I just said about chlorinating with an SWG, pretty much applies also to chlorinating with liquid chlorine.