What is the CH of your tap water?
It is probably pretty high if you need a water softener.
Many of us have plumbed our water softener to the autofill to help control CH. Sure, it regenerates more often, but using softened water keeps the CH of the pool at a relative constant.
My tap water CH is around 250. My entire pool volume evaporates as least once per year, so my CH would increase at least 250 every year. Using a bit more salt is worth it to me to not have to fully drain my pool every 2-3 years do to high CH. For my 12,000 gallon pool, thats about 2 bags of salt per year for the softener to produce the needed soft water for the autofill water. Maintainig a relatively constant CH also makes it easier to manage my CSI.