I know there have been discussions about the effects of water softening, and I just can't recall them at the moment but someone will come along soon, no doubt.
I can tell you that you could have all sorts of things in your well water, since wells are impacted by runoff. Phosphate is going to be something you could test for, as well as nitrate.
I'd rather take my water and pay to have it tested, since some of these companies that come and test your water for free have a lot of $$ riding on the assumed poor quality of your water, and they will find a way for your water to test poorly. Not all of them are like that, but I had one guy come out and he was telling me there was super high pH and nitrate in my water, and I'd better invest right away in his water purification system, but I have test kits and meters of my own, so he suddenly realized he had another appointment....