We used to have a water softener in our old house. I added salt myself.
Yes, it feels like you have a filmy substance on you while you shower. But, everyone’s hair was fuller. After we moved from that house and had no water softener anymore it seemed like my hair got thinner and I started to look like I was losing my hair. We recently stayed at my MIL’s house which has a water softener and sure enough, after two days of showers there my hair started to look fuller and thicker again. My wife also notices the difference in her hair being more thicker.
So, if you have thinning hair get a water softener. I even went so far as to look on the internet for shampoo that could simulate the effects of a water softener but no luck.